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["Topics","Sheet Link"]
["Sampling Distribution of Xbar1 - Xbar2","SDofDiffXbars!A1"]
["Confidence Interval for Difference Between 2 Population Means, Sigma1 and Sigma2 Known: Z","CI Sigma Known, z'!A1"]
["Hypothesis Testing for Difference Between 2 Population Means, Sigma1 and Sigma2 Known: Z","HT Sigma Known, z'!A1"]
["Confidence Interval for Difference Between 2 Population Means, Sigma1 and Sigma2 NOT Known: T","CI Sigma NOT Known, t'!A1"]
["Hypothesis Testing for Difference Between 2 Population Means, Sigma1 and Sigma2 NOT Known: T","HT Sigma NOT Known, t'!A1"]
["Matched Samples","HT & CI Matched Sample, t'!A1"]
["Completely Randomized Design","CRD(1)'!A1"]
["Analysis of Variance ANOVA","ANOVA-Long'!A1"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Whenever possible, equal sample size n1 = n2, are recommended."]
["Note about this:"]
["http://www.theanalysisfactor.com/when-unequal-sample-sizes-are-and-are-not-a-problem-in-anova/"]

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["Town 1",null,null,"N",{"$f":"COUNT(A2:A6)","v":5},null,null,null,"Town 2",null,null,"N",{"$f":"COUNT(I2:I6)","v":5},null,null,null,"Total Differences =",null,{"$f":"E3*M3","v":100},null,null,null,null,null,"Max",{"$f":"MAX(S5:S104,W5:W29)","v":0},null,null,"Sampling Distribution of Xbar1-Xbar2"]
[75000,null,null,"n1",2,null,null,null,43500,null,null,"n2",2,null,null,null,"Sample Differences:",null,null,null,"Pop Differences:",null,null,null,"Min",{"$f":"MIN(S5:S104,W5:W29)","v":0}]
[54800,null,null,"Combinations",{"$f":"COMBIN(E1,E2)","v":10},"All Possible Samples",null,null,65000,null,null,"Combinations",{"$f":"COMBIN(M1,M2)","v":10},"All Possible Samples"]
[18500,null,null,null,null,null,null,null,19000,null,null,null,null,null,null,null,"Town 1","Town 2","Difference",null,"Town 1","Town 2","Difference",null,"Lower","Upper","Label","Pop Frequency","Sample Frequency"]
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[29500,null,{"$f":"$A$2","v":75000},{"$f":"A3","v":54800},{"$f":"AVERAGE(C6:D6)","v":64900},null,null,null,34500,null,{"$f":"$I$2","v":43500},{"$f":"I3","v":65000},{"$f":"AVERAGE(K6:L6)","v":54250},null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q6)-1)/10)+1)","v":64900},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R6)-1,10)+1)","v":31250},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U6)-1)/5)+1)","v":75000},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V6)-1,5)+1)","v":65000},null,null,{"$f":"Z5","v":-55000},{"$f":"Y6+5000","v":-50000},{"$f":"TEXT(Y6,\"0,K\")&\" up to \"&TEXT(Z6,\"0,K\")","v":"-55K up to -50K"},{"$f":"COUNTIFS($W$5:$W$29,\">=\"&Y6,$W$5:$W$29,\"<\"&Z6)","v":0},{"$f":"COUNTIFS($S$5:$S$104,\">=\"&Y6,$S$5:$S$104,\"<\"&Z6)","v":0}]
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[null,null,{"$f":"A5","v":24250},{"$f":"A6","v":29500},26875,null,null,null,null,null,{"$f":"I5","v":25000},{"$f":"I6","v":34500},29750,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q15)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R15)-1,10)+1)","v":54250},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U15)-1)/5)+1)","v":18500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V15)-1,5)+1)","v":43500}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q16)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R16)-1,10)+1)","v":31250},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U16)-1)/5)+1)","v":18500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V16)-1,5)+1)","v":65000}]
[null,null,null,"Mean of all Means = μXbar = ",null,"Expected Value (Xbar) = E(Xbar)",null,null,null,null,null,"Mean of all Means = μXbar = ",{"$f":"AVERAGE(M6:M15)","v":37400},"Expected Value (Xbar) = E(Xbar)",null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q17)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R17)-1,10)+1)","v":34250},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U17)-1)/5)+1)","v":18500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V17)-1,5)+1)","v":19000}]
[null,null,null,"Pop Mean = μ = ",null,null,null,null,null,null,null,"Pop Mean = μ = ",{"$f":"AVERAGE(I2:I6)","v":37400},null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q18)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R18)-1,10)+1)","v":39000},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U18)-1)/5)+1)","v":18500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V18)-1,5)+1)","v":25000}]
[null,null,null,null,null,null,"n/N",null,null,null,null,null,null,null,"n/N",null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q19)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R19)-1,10)+1)","v":42000},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U19)-1)/5)+1)","v":18500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V19)-1,5)+1)","v":34500}]
[null,null,null,"Pop SD = Sigma =",null,null,null,null,null,null,null,"Pop SD = Sigma =",{"$f":"_xlfn.STDEV.P(I2:I6)","v":16122.654868228123},null,{"$f":"M2/M1","v":0.4},null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q20)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R20)-1,10)+1)","v":45000},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U20)-1)/5)+1)","v":24250},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V20)-1,5)+1)","v":43500}]
[null,null,null,"Standard Error of SDofXbar =",null," < Pop cuz it lists ALL possible samples",null,null,null,null,null,"Standard Error of SDofXbar =",{"$f":"_xlfn.STDEV.P(M6:M15)","v":9873.0694315395158}," < Pop cuz it lists ALL possible samples",null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q21)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R21)-1,10)+1)","v":49750},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U21)-1)/5)+1)","v":24250},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V21)-1,5)+1)","v":65000}]
["Standard Error =\nSigma/SQRT(n)*SQRT((N-n)/(N-1))",null,null,null,null,null,null,null,"Standard Error =\nSigma/SQRT(n)*SQRT((N-n)/(N-1))",null,null,null,{"$f":"M20/SQRT(M2)*SQRT((M1-M2)/(M1-1))","v":9873.0694315395122},null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q22)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R22)-1,10)+1)","v":22000},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U22)-1)/5)+1)","v":24250},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V22)-1,5)+1)","v":19000}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q23)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R23)-1,10)+1)","v":26750},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U23)-1)/5)+1)","v":24250},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V23)-1,5)+1)","v":25000}]
[null,null,null,"Pop Variance = Sigma^2 = s21",null,null,null,null,null,null,null,"Pop Variance = Sigma^2 = s22",{"$f":"M20^2","v":259940000},null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q24)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R24)-1,10)+1)","v":29750},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U24)-1)/5)+1)","v":24250},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V24)-1,5)+1)","v":34500}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q25)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R25)-1,10)+1)","v":54250},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U25)-1)/5)+1)","v":29500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V25)-1,5)+1)","v":43500}]
["Similar to what we did in video:",null,null,null,"Excel 2013 Statistical Analysis #43: Simple Random Sampling in Excel: Process & Theory ",null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q26)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R26)-1,10)+1)","v":31250},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U26)-1)/5)+1)","v":29500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V26)-1,5)+1)","v":65000}]
[null,null,null,null,"Excel 2013 Statistical Analysis #44: Sampling Distribution of Xbar and the Central Limit Theorem ",null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q27)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R27)-1,10)+1)","v":34250},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U27)-1)/5)+1)","v":29500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V27)-1,5)+1)","v":19000}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q28)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R28)-1,10)+1)","v":39000},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U28)-1)/5)+1)","v":29500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V28)-1,5)+1)","v":25000}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q29)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R29)-1,10)+1)","v":42000},null,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U29)-1)/5)+1)","v":29500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V29)-1,5)+1)","v":34500}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q30)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R30)-1,10)+1)","v":45000}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q31)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R31)-1,10)+1)","v":49750},null,null,null,null,null,null,null,null,null,"Check:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q32)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R32)-1,10)+1)","v":22000},null,null,"Mean of all Sample Differences = μXbar1-Xbar2 = ",null,null,null,"Expected Value (Xbar1 - Xbar2)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q33)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R33)-1,10)+1)","v":26750},null,null,"Pop Mean = μ1 - μ2 = "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q34)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R34)-1,10)+1)","v":29750},null,null,"Sample Size = n = "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q35)-1)/10)+1)","v":52250},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R35)-1,10)+1)","v":54250},null,null,"Pop Size"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q36)-1)/10)+1)","v":52250},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R36)-1,10)+1)","v":31250},null,null,null,null,null,null,null,"n/N"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q37)-1)/10)+1)","v":52250},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R37)-1,10)+1)","v":34250},null,null,null,null,"Pop SD = Sigma =",null,null,null," **Must use Finite Population Correction Factor when n/N > 0.05"]
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[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Video Reference for incrementing Numbers:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Excel Magic Trick 692: More About Incrementing Numbers In Formulas "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"https://www.youtube.com/watch?v=AIQbJAPMrEg"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Excel Magic Trick 650: Formula To Extract All Rows In Data Set Into 1 Column INDEX function "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"https://www.youtube.com/watch?v=KtIOwYNkUdE"]

{"sheet":"SDofDiffXbars (an)","index":2,"n_rows":110,"n_cols":29,"rows_kept":110,"cut":false,"hidden":false,"merged":[]}
["Town 1",null,null,"N",{"$f":"COUNT(A2:A6)","v":5},null,null,null,"Town 2",null,null,"N",{"$f":"COUNT(I2:I6)","v":5},null,null,null,"Total Differences =",null,{"$f":"E3*M3","v":100},null,null,null,null,null,"Max",{"$f":"MAX(S5:S104,W5:W29)","v":56000},null,null,"Sampling Distribution of Xbar1-Xbar2"]
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[54800,null,null,"Combinations",{"$f":"COMBIN(E1,E2)","v":10},"All Possible Samples",null,null,65000,null,null,"Combinations",{"$f":"COMBIN(M1,M2)","v":10},"All Possible Samples"]
[18500,null,null,null,null,null,null,null,19000,null,null,null,null,null,null,null,"Town 1","Town 2","Difference",null,"Town 1","Town 2","Difference",null,"Lower","Upper","Label","Pop Frequency","Sample Frequency"]
[24250,null,"SP 1","SP 2","Xbar",null,null,null,25000,null,"SP 1","SP 2","Xbar",null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q5)-1)/10)+1)","v":64900},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R5)-1,10)+1)","v":54250},{"$f":"Q5-R5","v":10650},null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U5)-1)/5)+1)","v":75000},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V5)-1,5)+1)","v":43500},{"$f":"U5-V5","v":31500},null,-60000,{"$f":"Y5+5000","v":-55000},{"$f":"TEXT(Y5,\"0,K\")&\" up to \"&TEXT(Z5,\"0,K\")","v":"-60K up to -55K"},{"$f":"COUNTIFS($W$5:$W$29,\">=\"&Y5,$W$5:$W$29,\"<\"&Z5)","v":0},{"$f":"COUNTIFS($S$5:$S$104,\">=\"&Y5,$S$5:$S$104,\"<\"&Z5)","v":0}]
[29500,null,{"$f":"$A$2","v":75000},{"$f":"A3","v":54800},{"$f":"AVERAGE(C6:D6)","v":64900},null,null,null,34500,null,{"$f":"$I$2","v":43500},{"$f":"I3","v":65000},{"$f":"AVERAGE(K6:L6)","v":54250},null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q6)-1)/10)+1)","v":64900},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R6)-1,10)+1)","v":31250},{"$f":"Q6-R6","v":33650},null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U6)-1)/5)+1)","v":75000},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V6)-1,5)+1)","v":65000},{"$f":"U6-V6","v":10000},null,{"$f":"Z5","v":-55000},{"$f":"Y6+5000","v":-50000},{"$f":"TEXT(Y6,\"0,K\")&\" up to \"&TEXT(Z6,\"0,K\")","v":"-55K up to -50K"},{"$f":"COUNTIFS($W$5:$W$29,\">=\"&Y6,$W$5:$W$29,\"<\"&Z6)","v":0},{"$f":"COUNTIFS($S$5:$S$104,\">=\"&Y6,$S$5:$S$104,\"<\"&Z6)","v":0}]
[null,null,75000,18500,{"$f":"AVERAGE(C7:D7)","v":46750},null,null,null,null,null,43500,19000,31250,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q7)-1)/10)+1)","v":64900},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R7)-1,10)+1)","v":34250},30650,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U7)-1)/5)+1)","v":75000},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V7)-1,5)+1)","v":19000},56000,null,{"$f":"Z6","v":-50000},{"$f":"Y7+5000","v":-45000},{"$f":"TEXT(Y7,\"0,K\")&\" up to \"&TEXT(Z7,\"0,K\")","v":"-50K up to -45K"},{"$f":"COUNTIFS($W$5:$W$29,\">=\"&Y7,$W$5:$W$29,\"<\"&Z7)","v":1},{"$f":"COUNTIFS($S$5:$S$104,\">=\"&Y7,$S$5:$S$104,\"<\"&Z7)","v":0}]
[null,null,75000,24250,49625,null,null,null,null,null,43500,25000,34250,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q8)-1)/10)+1)","v":64900},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R8)-1,10)+1)","v":39000},25900,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U8)-1)/5)+1)","v":75000},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V8)-1,5)+1)","v":25000},50000,null,-45000,-40000,"-45K up to -40K",1,0]
[null,null,75000,29500,52250,null,null,null,null,null,43500,34500,39000,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q9)-1)/10)+1)","v":64900},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R9)-1,10)+1)","v":42000},22900,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U9)-1)/5)+1)","v":75000},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V9)-1,5)+1)","v":34500},40500,null,-40000,-35000,"-40K up to -35K",1,0]
[null,null,{"$f":"$A$3","v":54800},{"$f":"A4","v":18500},36650,null,null,null,null,null,{"$f":"$I$3","v":65000},{"$f":"I4","v":19000},42000,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q10)-1)/10)+1)","v":64900},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R10)-1,10)+1)","v":45000},19900,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U10)-1)/5)+1)","v":54800},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V10)-1,5)+1)","v":43500},11300,null,-35000,-30000,"-35K up to -30K",0,2]
[null,null,54800,24250,39525,null,null,null,null,null,65000,25000,45000,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q11)-1)/10)+1)","v":64900},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R11)-1,10)+1)","v":49750},15150,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U11)-1)/5)+1)","v":54800},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V11)-1,5)+1)","v":65000},-10200,null,-30000,-25000,"-30K up to -25K",0,3]
[null,null,54800,29500,42150,null,null,null,null,null,65000,34500,49750,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q12)-1)/10)+1)","v":64900},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R12)-1,10)+1)","v":22000},42900,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U12)-1)/5)+1)","v":54800},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V12)-1,5)+1)","v":19000},35800,null,-25000,-20000,"-25K up to -20K",1,4]
[null,null,{"$f":"$A$4","v":18500},{"$f":"A5","v":24250},21375,null,null,null,null,null,{"$f":"$I$4","v":19000},{"$f":"I5","v":25000},22000,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q13)-1)/10)+1)","v":64900},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R13)-1,10)+1)","v":26750},38150,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U13)-1)/5)+1)","v":54800},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V13)-1,5)+1)","v":25000},29800,null,-20000,-15000,"-20K up to -15K",2,5]
[null,null,18500,29500,24000,null,null,null,null,null,19000,34500,26750,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q14)-1)/10)+1)","v":64900},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R14)-1,10)+1)","v":29750},35150,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U14)-1)/5)+1)","v":54800},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V14)-1,5)+1)","v":34500},20300,null,-15000,-10000,"-15K up to -10K",3,8]
[null,null,{"$f":"A5","v":24250},{"$f":"A6","v":29500},26875,null,null,null,null,null,{"$f":"I5","v":25000},{"$f":"I6","v":34500},29750,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q15)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R15)-1,10)+1)","v":54250},-7500,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U15)-1)/5)+1)","v":18500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V15)-1,5)+1)","v":43500},-25000,null,-10000,-5000,"-10K up to -5K",1,11]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q16)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R16)-1,10)+1)","v":31250},15500,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U16)-1)/5)+1)","v":18500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V16)-1,5)+1)","v":65000},-46500,null,-5000,0,"-5K up to 0K",3,11]
[null,null,null,"Mean of all Means = μXbar = ",{"$f":"AVERAGE(E6:E15)","v":40410},"Expected Value (Xbar) = E(Xbar)",null,null,null,null,null,"Mean of all Means = μXbar = ",{"$f":"AVERAGE(M6:M15)","v":37400},"Expected Value (Xbar) = E(Xbar)",null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q17)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R17)-1,10)+1)","v":34250},12500,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U17)-1)/5)+1)","v":18500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V17)-1,5)+1)","v":19000},-500,null,0,5000,"0K up to 5K",1,11]
[null,null,null,"Pop Mean = μ = ",{"$f":"AVERAGE(A2:A6)","v":40410},null,null,null,null,null,null,"Pop Mean = μ = ",{"$f":"AVERAGE(I2:I6)","v":37400},null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q18)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R18)-1,10)+1)","v":39000},7750,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U18)-1)/5)+1)","v":18500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V18)-1,5)+1)","v":25000},-6500,null,5000,10000,"5K up to 10K",1,10]
[null,null,null,null,null,null,"n/N",null,null,null,null,null,null,null,"n/N",null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q19)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R19)-1,10)+1)","v":42000},4750,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U19)-1)/5)+1)","v":18500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V19)-1,5)+1)","v":34500},-16000,null,10000,15000,"10K up to 15K",3,9]
[null,null,null,"Pop SD = Sigma =",{"$f":"_xlfn.STDEV.P(A2:A6)","v":21277.979227360855},null,{"$f":"E2/E1","v":0.4},null,null,null,null,"Pop SD = Sigma =",{"$f":"_xlfn.STDEV.P(I2:I6)","v":16122.654868228123},null,{"$f":"M2/M1","v":0.4},null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q20)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R20)-1,10)+1)","v":45000},1750,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U20)-1)/5)+1)","v":24250},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V20)-1,5)+1)","v":43500},-19250,null,15000,20000,"15K up to 20K",0,10]
[null,null,null,"Standard Error of SDofXbar =",{"$f":"_xlfn.STDEV.P(E6:E15)","v":13030.047966143486}," < Pop cuz it lists ALL possible samples",null,null,null,null,null,"Standard Error of SDofXbar =",{"$f":"_xlfn.STDEV.P(M6:M15)","v":9873.0694315395158}," < Pop cuz it lists ALL possible samples",null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q21)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R21)-1,10)+1)","v":49750},-3000,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U21)-1)/5)+1)","v":24250},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V21)-1,5)+1)","v":65000},-40750,null,20000,25000,"20K up to 25K",1,7]
["Standard Error =\nSigma/SQRT(n)*SQRT((N-n)/(N-1))",null,null,null,{"$f":"E20/SQRT(E2)*SQRT((E1-E2)/(E1-1))","v":13030.047966143486},null,null,null,"Standard Error =\nSigma/SQRT(n)*SQRT((N-n)/(N-1))",null,null,null,{"$f":"M20/SQRT(M2)*SQRT((M1-M2)/(M1-1))","v":9873.0694315395122},null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q22)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R22)-1,10)+1)","v":22000},24750,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U22)-1)/5)+1)","v":24250},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V22)-1,5)+1)","v":19000},5250,null,25000,30000,"25K up to 30K",1,3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q23)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R23)-1,10)+1)","v":26750},20000,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U23)-1)/5)+1)","v":24250},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V23)-1,5)+1)","v":25000},-750,null,30000,35000,"30K up to 35K",1,3]
[null,null,null,"Pop Variance = Sigma^2 = s21",{"$f":"E20^2","v":452752400},null,null,null,null,null,null,"Pop Variance = Sigma^2 = s22",{"$f":"M20^2","v":259940000},null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q24)-1)/10)+1)","v":46750},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R24)-1,10)+1)","v":29750},17000,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U24)-1)/5)+1)","v":24250},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V24)-1,5)+1)","v":34500},-10250,null,35000,40000,"35K up to 40K",1,2]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q25)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R25)-1,10)+1)","v":54250},-4625,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U25)-1)/5)+1)","v":29500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V25)-1,5)+1)","v":43500},-14000,null,40000,45000,"40K up to 45K",1,1]
["Similar to what we did in video:",null,null,null,"Excel 2013 Statistical Analysis #43: Simple Random Sampling in Excel: Process & Theory ",null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q26)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R26)-1,10)+1)","v":31250},18375,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U26)-1)/5)+1)","v":29500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V26)-1,5)+1)","v":65000},-35500,null,45000,50000,"45K up to 50K",0,0]
[null,null,null,null,"Excel 2013 Statistical Analysis #44: Sampling Distribution of Xbar and the Central Limit Theorem ",null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q27)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R27)-1,10)+1)","v":34250},15375,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U27)-1)/5)+1)","v":29500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V27)-1,5)+1)","v":19000},10500,null,50000,55000,"50K up to 55K",1,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q28)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R28)-1,10)+1)","v":39000},10625,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U28)-1)/5)+1)","v":29500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V28)-1,5)+1)","v":25000},4500,null,55000,60000,"55K up to 60K",1,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q29)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R29)-1,10)+1)","v":42000},7625,null,{"$f":"INDEX($A$2:$A$6,INT((ROWS(U$5:U29)-1)/5)+1)","v":29500},{"$f":"INDEX($I$2:$I$6,MOD(ROWS(V$5:V29)-1,5)+1)","v":34500},-5000]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q30)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R30)-1,10)+1)","v":45000},4625]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q31)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R31)-1,10)+1)","v":49750},-125,null,null,null,null,null,null,null,null,"Check:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q32)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R32)-1,10)+1)","v":22000},27625,null,"Mean of all Sample Differences = μXbar1-Xbar2 = ",null,null,{"$f":"AVERAGE(S5:S104)","v":3010},"Expected Value (Xbar1 - Xbar2)",null,null,{"$f":"AVERAGE(E6:E15)-AVERAGE(M6:M15)","v":3010},{"$f":"AVERAGE(Q5:Q104)-AVERAGE(R5:R104)","v":3010}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q33)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R33)-1,10)+1)","v":26750},22875,null,"Pop Mean = μ1 - μ2 = ",null,null,{"$f":"AVERAGE(W5:W29)","v":3010},null,null,null,{"$f":"AVERAGE(A2:A6)-AVERAGE(I2:I6)","v":3010},{"$f":"AVERAGE(U5:U29)-AVERAGE(V5:V29)","v":3010}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q34)-1)/10)+1)","v":49625},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R34)-1,10)+1)","v":29750},19875,null,"Sample Size = n = ",null,null,{"$f":"E2","v":2}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q35)-1)/10)+1)","v":52250},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R35)-1,10)+1)","v":54250},-2000,null,"Pop Size",null,null,{"$f":"E1","v":5}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q36)-1)/10)+1)","v":52250},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R36)-1,10)+1)","v":31250},21000,null,null,null,null,null,null,"n/N"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q37)-1)/10)+1)","v":52250},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R37)-1,10)+1)","v":34250},18000,null,null,null,"Pop SD = Sigma =",null,null,{"$f":"X34/X35","v":0.4}," **Must use Finite Population Correction Factor when n/N > 0.05"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"INDEX($E$6:$E$15,INT((ROWS(Q$5:Q38)-1)/10)+1)","v":52250},{"$f":"INDEX($M$6:$M$15,MOD(ROWS(R$5:R38)-1,10)+1)","v":39000},13250,null,null,null,"Standard Error of SDofXbar1-Xbar2 =",{"$f":"_xlfn.STDEV.P(S5:S104)","v":16348.077868667007}," < Pop cuz it lists ALL possible samples"]
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[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Video Reference for incrementing Numbers:"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Excel Magic Trick 692: More About Incrementing Numbers In Formulas "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"https://www.youtube.com/watch?v=AIQbJAPMrEg"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Excel Magic Trick 650: Formula To Extract All Rows In Data Set Into 1 Column INDEX function "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"https://www.youtube.com/watch?v=KtIOwYNkUdE"]

{"sheet":"CI Sigma Known, z","index":3,"n_rows":47,"n_cols":12,"rows_kept":47,"cut":false,"hidden":false,"merged":[]}
["Two cities, Bradford and Kane are separated only by the Conewango River."]
["A random sample of annual incomes from both cities was taken."]
["Sigma (Pop SD) is known from past data to be: Bradford s = $6000, Kane s = $7000."]
["Build a 95% Confidence Interval for the difference between the two city population annual income means"]
[]
["Sample 1",null,"Sample 2",null,null,"Sample 1","Sample 2"]
["Bradford",null,"Kane",null,"City",{"$f":"A7","v":"Bradford"},{"$f":"C7","v":"Kane"}]
[30316,null,29652,null,"Sigma = Pop SD = s ="]
[38832,null,30613,null,"Sample Size = n =",null,null,null,{"$f":"IF(_xlfn.ISFORMULA(G9),\" \"&_xlfn.FORMULATEXT(G9),\"\")","v":""}]
[44320,null,31617,null,"Sample Mean = Xbar",null,null,null,""]
[34076,null,33665,null,"Pop Variance = s2 =",null,null,null,""]
[27061,null,37109,null,"Pop Variance/ Sample Size = s2/n =",null,null,null,""]
[37948,null,35487]
[50215,null,28702,null,"Population Difference = m1 -  m2"]
[33458,null,28368,null,"Point Estimate for Pop. Difference ==>> Xbar1 - Xbar2 =",null,null,{"$f":"IF(_xlfn.ISFORMULA(F15),\" \"&_xlfn.FORMULATEXT(F15),\"\")","v":""}]
[39553,null,20866,null,"Confidence Level"]
[31134,null,31960,null,"Alpha",null,null,{"$f":"IF(_xlfn.ISFORMULA(F17),\" \"&_xlfn.FORMULATEXT(F17),\"\")","v":""}]
[35329,null,38462,null,"Alpha/2",null,null,""]
[43280,null,49736,null,"Standard Error =",null,null,"",null,null,null,"Standard Deviation of the Sampling Distribution of Xbar1 - Xbar2"]
[44657,null,29799,null,"Z Upper",null,null,""]
[40339,null,36454,null,"Margin of Error",null,null,"",null,null,null,"Margin of Error = Z Upper * SE"]
[38522,null,26958,null,"Lower Limit",null,null,"",null,null,null,"Z Upper +/- Margin of Error"]
[36060,null,35762,null,"Upper Limit",null,null,""]
[39703,null,39513]
[35383,null,30460,null,{"$f":"IF(F23=\"\",\"\",\"We are \"&TEXT(F16,\"0%\")&\" sure that the population difference between the incomes in \"&A7&\" and \"&C7&\" are between \"&DOLLAR(F22,0)&\" and \"&DOLLAR(F23,0))","v":""}]
[36913,null,42200,null,{"$f":"IF(F23=\"\",\"\",\"The difference between Bradford and Kane Annual Income is about \"&DOLLAR(F15,0)&\" with a margin of error of \"&DOLLAR(F21,0))","v":""}]
[22736,null,22003,null,{"$f":"IF(F23=\"\",\"\",\"If we constructed 100 confidence intervals, about 95 of them would contain the population difference and 5 would not.\")","v":""}]
[39523,null,40513]
[28428,null,34304]
[35660,null,33118]
[37371,null,30886]
[39667,null,43729]
[34245,null,33613]
[34026,null,41491]
[37524,null,44969]
[44202,null,38931]
[45706,null,26953]
[35585,null,41270]
[33164,null,39754]
[35804,null,39949]
[39773,null,35829]
[40127,null,40514]
[45767]
[47522]
[48127]
[33478]
[44866]

{"sheet":"CI Sigma Known, z (an)","index":4,"n_rows":47,"n_cols":12,"rows_kept":47,"cut":false,"hidden":false,"merged":[]}
["Two cities, Bradford and Kane are separated only by the Conewango River."]
["A random sample of annual incomes from both cities was taken."]
["Sigma (Pop SD) is known from past data to be: Bradford s = $6000, Kane s = $7000."]
["Build a 95% Confidence Interval for the difference between the two city population annual income means"]
[]
["Sample 1",null,"Sample 2",null,null,"Sample 1","Sample 2"]
["Bradford",null,"Kane",null,"City",{"$f":"A7","v":"Bradford"},{"$f":"C7","v":"Kane"}]
[30316,null,29652,null,"Sigma = Pop SD = s =",6000,7000]
[38832,null,30613,null,"Sample Size = n =",{"$f":"COUNT(A8:A47)","v":40},{"$f":"COUNT(C8:C42)","v":35},null,{"$f":"IF(_xlfn.ISFORMULA(G9),\" \"&_xlfn.FORMULATEXT(G9),\"\")","v":" =COUNT(C8:C42)"}]
[44320,null,31617,null,"Sample Mean = Xbar",{"$f":"AVERAGE(A8:A47)","v":38010},{"$f":"AVERAGE(C8:C42)","v":35005.971428571429},null," =AVERAGE(C8:C42)"]
[34076,null,33665,null,"Pop Variance = s2 =",{"$f":"F8^2","v":36000000},{"$f":"G8^2","v":49000000},null," =G8^2"]
[27061,null,37109,null,"Pop Variance/ Sample Size = s2/n =",{"$f":"F11/F9","v":900000},{"$f":"G11/G9","v":1400000},null," =G11/G9"]
[37948,null,35487]
[50215,null,28702,null,"Population Difference = m1 -  m2"]
[33458,null,28368,null,"Point Estimate for Pop. Difference ==>> Xbar1 - Xbar2 =",{"$f":"F10-G10","v":3004.028571428571},null,{"$f":"IF(_xlfn.ISFORMULA(F15),\" \"&_xlfn.FORMULATEXT(F15),\"\")","v":" =F10-G10"}]
[39553,null,20866,null,"Confidence Level",0.95]
[31134,null,31960,null,"Alpha",{"$f":"1-F16","v":5.0000000000000044E-2},null,{"$f":"IF(_xlfn.ISFORMULA(F17),\" \"&_xlfn.FORMULATEXT(F17),\"\")","v":" =1-F16"}]
[35329,null,38462,null,"Alpha/2",{"$f":"F17/2","v":2.5000000000000022E-2},null," =F17/2"]
[43280,null,49736,null,"Standard Error =",{"$f":"SQRT(SUM(F12:G12))","v":1516.57508881031},null," =SQRT(SUM(F12:G12))",null,null,null,"Standard Deviation of the Sampling Distribution of Xbar1 - Xbar2"]
[44657,null,29799,null,"Z Upper",{"$f":"_xlfn.NORM.S.INV(1-F18)","v":1.9599639845400536},null," =NORM.S.INV(1-F18)"]
[40339,null,36454,null,"Margin of Error",{"$f":"F20*F19","v":2972.4325539188408},null," =F20*F19",null,null,null,"Margin of Error = Z Upper * SE"]
[38522,null,26958,null,"Lower Limit",{"$f":"F15-F21","v":31.596017509730245},null," =F15-F21",null,null,null,"Z Upper +/- Margin of Error"]
[36060,null,35762,null,"Upper Limit",{"$f":"F15+F21","v":5976.4611253474122},null," =F15+F21"]
[39703,null,39513]
[35383,null,30460,null,{"$f":"IF(F23=\"\",\"\",\"We are \"&TEXT(F16,\"0%\")&\" sure that the population difference between the incomes in \"&A7&\" and \"&C7&\" are between \"&DOLLAR(F22,0)&\" and \"&DOLLAR(F23,0))","v":"We are 95% sure that the population difference between the incomes in Bradford and Kane are between $32 and $5,976"}]
[36913,null,42200,null,{"$f":"IF(F23=\"\",\"\",\"The difference between Bradford and Kane Annual Income is about \"&DOLLAR(F15,0)&\" with a margin of error of \"&DOLLAR(F21,0))","v":"The difference between Bradford and Kane Annual Income is about $3,004 with a margin of error of $2,972"}]
[22736,null,22003,null,{"$f":"IF(F23=\"\",\"\",\"If we constructed 100 confidence intervals, about 95 of them would contain the population difference and 5 would not.\")","v":"If we constructed 100 confidence intervals, about 95 of them would contain the population difference and 5 would not."}]
[39523,null,40513]
[28428,null,34304]
[35660,null,33118]
[37371,null,30886]
[39667,null,43729]
[34245,null,33613]
[34026,null,41491]
[37524,null,44969]
[44202,null,38931]
[45706,null,26953]
[35585,null,41270]
[33164,null,39754]
[35804,null,39949]
[39773,null,35829]
[40127,null,40514]
[45767]
[47522]
[48127]
[33478]
[44866]

{"sheet":"HT Sigma Known, z","index":5,"n_rows":47,"n_cols":14,"rows_kept":47,"cut":false,"hidden":false,"merged":[]}
["Two cities, Bradford and Kane are separated only by the Conewango River."]
["A random sample of annual incomes from both cities was taken."]
["Sigma (Pop SD) is known from past data to be: Bradford s = $6000, Kane s = $7000."]
["At an alpha of 5% can we conclude that Bradford's Annual Income is more than Kane's?",null,null,null,null,null,null," >"]
[]
["Sample 1",null,"Sample 2",null,null,"Sample 1","Sample 2"]
["Bradford",null,"Kane",null,"Cities",{"$f":"A7","v":"Bradford"},{"$f":"C7","v":"Kane"}]
[30316,null,29652,null,"Sigma = Pop SD = s =",null,null,null,"Formulas for Sample 2"]
[38832,null,30613,null,"Sample Mean = Xbar",null,null,null,{"$f":"IF(G9=\"\",\"\",\" \"&_xlfn.FORMULATEXT(G9))","v":""}]
[44320,null,31617,null,"Count = n =",null,null,null,""]
[34076,null,33665,null,"Pop Variance",null,null,null,""]
[27061,null,37109,null,"Variance/n",null,null,null,""]
[37948,null,35487]
[50215,null,28702,null,"Step 1: List Null and Alternative Hypotheses"]
[33458,null,28368,null,"H0 : m1 - m2"]
[39553,null,20866,null,"Ha : m1 - m2"]
[31134,null,31960]
[35329,null,38462,null,"Hypothesized Pop Difference"]
[43280,null,49736]
[44657,null,29799,null,"Step 2: Pick Level of Significance = Alpha (Risk that H0 is TRUE, but we Reject it)"]
[40339,null,36454,null,"Alpha"]
[38522,null,26958]
[36060,null,35762,null,"Step 3: Sample, Calculate, Draw Picture, Calculate Test Statistic"]
[39703,null,39513,null,"SE",null,null,{"$f":"IF(F24=\"\",\"\",\" \"&_xlfn.FORMULATEXT(F24))","v":""},null,null,"SQRT(Var1/n1 + Var2/n2)",null,null,"Standard Deviation of the Sampling Distribution of Xbar1 - Xbar2"]
[35383,null,30460,null,"Test Statistic",null,null,{"$f":"IF(F25=\"\",\"\",\" \"&_xlfn.FORMULATEXT(F25))","v":""},null,null,"(Xbar1-Xbar2-D0)/SE"]
[36913,null,42200]
[22736,null,22003,null,"Step 4: Create Rules for Critical Value and p-value"]
[39523,null,40513,null,"If our calculated Test Statistic is greater than our Critical Value, We Reject H0 and Accept Ha, Otherwise, We Fail to Reject H0"]
[28428,null,34304,null,"Critical Value",null,null,{"$f":"IF(F29=\"\",\"\",\" \"&_xlfn.FORMULATEXT(F29))","v":""}]
[35660,null,33118,null,"If the p-value is smaller than our Alpha, We Reject H0 and Accept Ha, Otherwise, We Fail to Reject H0"]
[37371,null,30886,null,"p-value",null,null,{"$f":"IF(F31=\"\",\"\",\" \"&_xlfn.FORMULATEXT(F31))","v":""}]
[39667,null,43729]
[34245,null,33613,null,"Step 5: Write Conclusion"]
[34026,null,41491,null,{"$f":"IF(F31=\"\",\"\",\"Because the calculated Test Statistic is greater than our Critical Value, We Reject H0 and Accept Ha. It is reasonable to assume that the Mean Income in Bradford is more than in Kane.\")","v":""}]
[37524,null,44969,null,{"$f":"IF(F31=\"\",\"\",\"Because the p-values is smaller than the alpha, We Reject H0 and Accept Ha. It is reasonable to assume that the Mean Income in Bradford is more than in Kane.\")","v":""}]
[44202,null,38931,null,{"$f":"IF(F31=\"\",\"\",\"The sample evidence seems to suggest that the Mean Income in Bradford is more than in Kane.\")","v":""}]
[45706,null,26953,null,{"$f":"IF(F31=\"\",\"\",\"We do run a 5% risk that we have rejected H0 even though it was true.\")","v":""}]
[35585,null,41270]
[33164,null,39754]
[35804,null,39949]
[39773,null,35829]
[40127,null,40514]
[45767]
[47522]
[48127]
[33478]
[44866]

{"sheet":"HT Sigma Known, z (an)","index":6,"n_rows":52,"n_cols":14,"rows_kept":52,"cut":false,"hidden":false,"merged":[]}
["Two cities, Bradford and Kane are separated only by the Conewango River."]
["A random sample of annual incomes from both cities was taken."]
["Sigma (Pop SD) is known from past data to be: Bradford s = $6000, Kane s = $7000."]
["At an alpha of 5% can we conclude that Bradford's Annual Income is more than Kane's?",null,null,null,null,null,null," >"]
[]
["Sample 1",null,"Sample 2",null,null,"Sample 1","Sample 2"]
["Bradford",null,"Kane",null,"Cities",{"$f":"A7","v":"Bradford"},{"$f":"C7","v":"Kane"}]
[30316,null,29652,null,"Sigma = Pop SD = s =",6000,7000,null,"Formulas for Sample 2"]
[38832,null,30613,null,"Sample Mean = Xbar",{"$f":"AVERAGE(A8:A47)","v":38010},{"$f":"AVERAGE(C8:C42)","v":35005.971428571429},null,{"$f":"IF(G9=\"\",\"\",\" \"&_xlfn.FORMULATEXT(G9))","v":" =AVERAGE(C8:C42)"}]
[44320,null,31617,null,"Count = n =",{"$f":"COUNT(A8:A47)","v":40},{"$f":"COUNT(C8:C42)","v":35},null," =COUNT(C8:C42)"]
[34076,null,33665,null,"Pop Variance",{"$f":"F8^2","v":36000000},{"$f":"G8^2","v":49000000},null," =G8^2"]
[27061,null,37109,null,"Variance/n",{"$f":"F11/F10","v":900000},{"$f":"G11/G10","v":1400000},null," =G11/G10"]
[37948,null,35487]
[50215,null,28702,null,"Step 1: List Null and Alternative Hypotheses"]
[33458,null,28368,null,"H0 : m1 - m2"," <=",{"$f":"$F$18","v":0}]
[39553,null,20866,null,"Ha : m1 - m2"," >",0]
[31134,null,31960]
[35329,null,38462,null,"Hypothesized Pop Difference",0]
[43280,null,49736]
[44657,null,29799,null,"Step 2: Pick Level of Significance = Alpha (Risk that H0 is TRUE, but we Reject it)"]
[40339,null,36454,null,"Alpha",0.05]
[38522,null,26958]
[36060,null,35762,null,"Step 3: Sample, Calculate, Draw Picture, Calculate Test Statistic"]
[39703,null,39513,null,"SE",{"$f":"SQRT(SUM(F12:G12))","v":1516.57508881031},null,{"$f":"IF(F24=\"\",\"\",\" \"&_xlfn.FORMULATEXT(F24))","v":" =SQRT(SUM(F12:G12))"},null,null,"SQRT(Var1/n1 + Var2/n2)",null,null,"Standard Deviation of the Sampling Distribution of Xbar1 - Xbar2"]
[35383,null,30460,null,"Test Statistic",{"$f":"(F9-G9-F18)/F24","v":1.9807977815230411},null,{"$f":"IF(F25=\"\",\"\",\" \"&_xlfn.FORMULATEXT(F25))","v":" =(F9-G9-F18)/F24"},null,null,"(Xbar1-Xbar2-D0)/SE"]
[36913,null,42200]
[22736,null,22003,null,"Step 4: Create Rules for Critical Value and p-value"]
[39523,null,40513,null,"If our calculated Test Statistic is greater than our Critical Value, We Reject H0 and Accept Ha, Otherwise, We Fail to Reject H0"]
[28428,null,34304,null,"Critical Value",{"$f":"_xlfn.NORM.S.INV(1-F21)","v":1.6448536269514715},null,{"$f":"IF(F29=\"\",\"\",\" \"&_xlfn.FORMULATEXT(F29))","v":" =NORM.S.INV(1-F21)"}]
[35660,null,33118,null,"If the p-value is smaller than our Alpha, We Reject H0 and Accept Ha, Otherwise, We Fail to Reject H0"]
[37371,null,30886,null,"p-value",{"$f":"1-_xlfn.NORM.S.DIST(F25,1)","v":2.380697785558894E-2},null,{"$f":"IF(F31=\"\",\"\",\" \"&_xlfn.FORMULATEXT(F31))","v":" =1-NORM.S.DIST(F25,1)"}]
[39667,null,43729]
[34245,null,33613,null,"Step 5: Write Conclusion"]
[34026,null,41491,null,{"$f":"IF(F31=\"\",\"\",\"Because the calculated Test Statistic is greater than our Critical Value, We Reject H0 and Accept Ha. It is reasonable to assume that the Mean Income in Bradford is more than in Kane.\")","v":"Because the calculated Test Statistic is greater than our Critical Value, We Reject H0 and Accept Ha. It is reasonable to assume that the Mean Income in Bradford is more than in Kane."}]
[37524,null,44969,null,{"$f":"IF(F31=\"\",\"\",\"Because the p-values is smaller than the alpha, We Reject H0 and Accept Ha. It is reasonable to assume that the Mean Income in Bradford is more than in Kane.\")","v":"Because the p-values is smaller than the alpha, We Reject H0 and Accept Ha. It is reasonable to assume that the Mean Income in Bradford is more than in Kane."}]
[44202,null,38931,null,{"$f":"IF(F31=\"\",\"\",\"The sample evidence seems to suggest that the Mean Income in Bradford is more than in Kane.\")","v":"The sample evidence seems to suggest that the Mean Income in Bradford is more than in Kane."}]
[45706,null,26953,null,{"$f":"IF(F31=\"\",\"\",\"We do run a 5% risk that we have rejected H0 even though it was true.\")","v":"We do run a 5% risk that we have rejected H0 even though it was true."}]
[35585,null,41270]
[33164,null,39754]
[35804,null,39949]
[39773,null,35829,null,"z-Test: Two Sample for Means"]
[40127,null,40514]
[45767,null,null,null,null,"Bradford","Kane"]
[47522,null,null,null,"Mean",38010,35005.971428571429]
[48127,null,null,null,"Known Variance",36000000,49000000]
[33478,null,null,null,"Observations",40,35]
[44866,null,null,null,"Hypothesized Mean Difference",0]
[null,null,null,null,"z",1.9807977815230411]
[null,null,null,null,"P(Z<=z) one-tail",2.380697785558894E-2]
[null,null,null,null,"z Critical one-tail",1.6448536269514715]
[null,null,null,null,"P(Z<=z) two-tail",4.761395571117788E-2]
[null,null,null,null,"z Critical two-tail",1.9599639845400536]

{"sheet":"CI Sigma NOT Known, t","index":7,"n_rows":34,"n_cols":8,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
["A recent EPA study compared the highway fuel economy of domestic and imported compact cars"]
[{"$f":"\"A sample of \"&COUNT(A9:A28)&\" imported compact cars revealed a mean of \"&ROUND(AVERAGE(A9:A28),2)&\" MPG with a standard deviation of \"&ROUND(_xlfn.STDEV.S(A9:A28),2)&\" MPG\"","v":"A sample of 20 imported compact cars revealed a mean of 36.52 MPG with a standard deviation of 3.43 MPG"}]
[{"$f":"\"A sample of \"&COUNT(B9:B28)&\" domestic compact cars revealed a mean of \"&ROUND(AVERAGE(B9:B28),2)&\" MPG with a standard deviation of \"&ROUND(_xlfn.STDEV.S(B9:B28),2)&\" MPG\"","v":"A sample of 20 domestic compact cars revealed a mean of 33.83 MPG with a standard deviation of 2.33 MPG"}]
["Samples are independent, Distributions for samples are normal ."]
["At the 95% Confidence Level, construct a Confidence Interval for the Population Difference between Imported Compact Auto MPG and Domestic Compact Auto MPG"]
[]
["Sample 1","Sample 2",null,null,"Sample 1","Sample 2"]
["Imported MPG","Domestic MPG",null,null,"Imported MPG","Domestic MPG",null,"Sample 2 Formulas"]
[31.07,35.729999999999997,null,"Sample Size = n =",null,null,null,{"$f":"IF(_xlfn.ISFORMULA(F9),\" \"&_xlfn.FORMULATEXT(F9),\"\")","v":""}]
[38.71,35.43,null,"n -1 =",null,null,null,""]
[34.369999999999997,34.04,null,"Sample Mean = Xbar =",null,null,"MPG",""]
[37.47,33.01,null,"Sample Standard Deviation = s =",null,null,"MPG",""]
[40.700000000000003,34.81,null,"Sample Variance = SVar = s^2 =",null,null,null,""]
[32.979999999999997,34.97,null,"SVar/n = S^2/n =",null,null,null,""]
[34.76,28.35]
[40.61,31.87,null,"Point Estimate of μ1 - μ2 = Xbar1 - Xbar2 =",null,null,"Sample 2 Formulas"]
[35.54,34.78,null,"Point Estimate = Xbar1 - Xbar2 =",null,"MPG",{"$f":"IF(_xlfn.ISFORMULA(E17),\" \"&_xlfn.FORMULATEXT(E17),\"\")","v":""}]
[37.78,31.27,null,"SE = ",null,"MPG",""]
[32.47,38.229999999999997,null,"Degrees of Freedom = df =",null,null,""]
[36,31.11,null,"Confidence Level/Coefficient ="]
[36.08,33.83,null,"Alpha =",null,null,{"$f":"IF(_xlfn.ISFORMULA(E21),\" \"&_xlfn.FORMULATEXT(E21),\"\")","v":""}]
[31.15,33.44,null,"Alpha/2 = ",null,null,""]
[37.65,34.340000000000003,null,"Upper t = ta/2 = # SD =",null,null,""]
[44.14,38.07,null,"Margin of Error =",null,"MPG",""]
[33.81,33.880000000000003,null,"T Upper =",null,"MPG",""]
[37.93,31.58,null,"T Lower =",null,"MPG",""]
[40.659999999999997,35.06]
[36.49,32.700000000000003,null,{"$f":"IF(E26=\"\",\"\",\"We are \"&TEXT($E$20,\"0%\")&\" that the population difference between Imported Compact Auto MPG and\")","v":""}]
[null,null,null,{"$f":"IF(E26=\"\",\"\",\"Domestic Compact Auto MPG is between \"&ROUND($E$25,2)&\" and \"&ROUND($E$26,2)&\" MPG\")","v":""}]
[]
[null,null,null,{"$f":"IF(E26=\"\",\"\",\"We are \"&TEXT($E$20,\"0%\")&\" that the population difference between Imported Compact Auto MPG and\")","v":""}]
[null,null,null,{"$f":"IF(E26=\"\",\"\",\"Domestic Compact Auto MPG is \"&ROUND(E17,2)&\" with a margin of error of \"&ROUND(E24,2)&\" MPG\")","v":""}]
[]
[null,null,null,{"$f":"IF(E26=\"\",\"\",\"We do run a 5% risk that our population difference is not in our interval.\")","v":""}]

{"sheet":"CI Sigma NOT Known, t (an)","index":8,"n_rows":34,"n_cols":8,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
["A recent EPA study compared the highway fuel economy of domestic and imported compact cars"]
[{"$f":"\"A sample of \"&COUNT(A9:A28)&\" imported compact cars revealed a mean of \"&ROUND(AVERAGE(A9:A28),2)&\" MPG with a standard deviation of \"&ROUND(_xlfn.STDEV.S(A9:A28),2)&\" MPG\"","v":"A sample of 20 imported compact cars revealed a mean of 36.52 MPG with a standard deviation of 3.43 MPG"}]
[{"$f":"\"A sample of \"&COUNT(B9:B28)&\" domestic compact cars revealed a mean of \"&ROUND(AVERAGE(B9:B28),2)&\" MPG with a standard deviation of \"&ROUND(_xlfn.STDEV.S(B9:B28),2)&\" MPG\"","v":"A sample of 20 domestic compact cars revealed a mean of 33.83 MPG with a standard deviation of 2.33 MPG"}]
["Samples are independent, Distributions for samples are normal ."]
["At the 95% Confidence Level, construct a Confidence Interval for the Population Difference between Imported Compact Auto MPG and Domestic Compact Auto MPG"]
[]
["Sample 1","Sample 2",null,null,"Sample 1","Sample 2"]
["Imported MPG","Domestic MPG",null,null,"Imported MPG","Domestic MPG",null,"Sample 2 Formulas"]
[31.07,35.729999999999997,null,"Sample Size = n =",{"$f":"COUNT(A9:A28)","v":20},{"$f":"COUNT(B9:B28)","v":20},null,{"$f":"IF(_xlfn.ISFORMULA(F9),\" \"&_xlfn.FORMULATEXT(F9),\"\")","v":" =COUNT(B9:B28)"}]
[38.71,35.43,null,"n -1 =",{"$f":"E9-1","v":19},{"$f":"F9-1","v":19},null," =F9-1"]
[34.369999999999997,34.04,null,"Sample Mean = Xbar =",{"$f":"AVERAGE(A9:A28)","v":36.518499999999996},{"$f":"AVERAGE(B9:B28)","v":33.82500000000001},"MPG"," =AVERAGE(B9:B28)"]
[37.47,33.01,null,"Sample Standard Deviation = s =",{"$f":"_xlfn.STDEV.S(A9:A28)","v":3.4329567967600547},{"$f":"_xlfn.STDEV.S(B9:B28)","v":2.3337016000111781},"MPG"," =STDEV.S(B9:B28)"]
[40.700000000000003,34.81,null,"Sample Variance = SVar = s^2 =",{"$f":"E12^2","v":11.785192368421056},{"$f":"F12^2","v":5.4461631578947323},null," =F12^2"]
[32.979999999999997,34.97,null,"SVar/n = S^2/n =",{"$f":"E13/E9","v":0.58925961842105279},{"$f":"F13/F9","v":0.27230815789473661},null," =F13/F9"]
[34.76,28.35]
[40.61,31.87,null,"Point Estimate of μ1 - μ2 = Xbar1 - Xbar2 =",null,null,"Sample 2 Formulas"]
[35.54,34.78,null,"Point Estimate = Xbar1 - Xbar2 =",{"$f":"E11-F11","v":2.693499999999986},"MPG",{"$f":"IF(_xlfn.ISFORMULA(E17),\" \"&_xlfn.FORMULATEXT(E17),\"\")","v":" =E11-F11"}]
[37.78,31.27,null,"SE = ",{"$f":"SQRT(SUM(E14:F14))","v":0.92820675300053135},"MPG"," =SQRT(SUM(E14:F14))"]
[32.47,38.229999999999997,null,"Degrees of Freedom = df =",{"$f":"SUM(E14:F14)^2/SUM(E14^2/E10,F14^2/F10)","v":33.470329535142355},null," =SUM(E14:F14)^2/SUM(E14^2/E10,F14^2/F10)"]
[36,31.11,null,"Confidence Level/Coefficient =",0.95]
[36.08,33.83,null,"Alpha =",{"$f":"1-E20","v":5.0000000000000044E-2},null,{"$f":"IF(_xlfn.ISFORMULA(E21),\" \"&_xlfn.FORMULATEXT(E21),\"\")","v":" =1-E20"}]
[31.15,33.44,null,"Alpha/2 = ",{"$f":"E21/2","v":2.5000000000000022E-2},null," =E21/2"]
[37.65,34.340000000000003,null,"Upper t = ta/2 = # SD =",{"$f":"_xlfn.T.INV(1-E22,E19)","v":2.0345152974493379},null," =T.INV(1-E22,E19)"]
[44.14,38.07,null,"Margin of Error =",{"$f":"E23*E18","v":1.8884508381753602},"MPG"," =E23*E18"]
[33.81,33.880000000000003,null,"T Upper =",{"$f":"E17+E24","v":4.581950838175346},"MPG"," =E17+E24"]
[37.93,31.58,null,"T Lower =",{"$f":"E17-E24","v":0.80504916182462583},"MPG"," =E17-E24"]
[40.659999999999997,35.06]
[36.49,32.700000000000003,null,{"$f":"IF(E26=\"\",\"\",\"We are \"&TEXT($E$20,\"0%\")&\" that the population difference between Imported Compact Auto MPG and\")","v":"We are 95% that the population difference between Imported Compact Auto MPG and"}]
[null,null,null,{"$f":"IF(E26=\"\",\"\",\"Domestic Compact Auto MPG is between \"&ROUND($E$25,2)&\" and \"&ROUND($E$26,2)&\" MPG\")","v":"Domestic Compact Auto MPG is between 4.58 and 0.81 MPG"}]
[]
[null,null,null,{"$f":"IF(E26=\"\",\"\",\"We are \"&TEXT($E$20,\"0%\")&\" that the population difference between Imported Compact Auto MPG and\")","v":"We are 95% that the population difference between Imported Compact Auto MPG and"}]
[null,null,null,{"$f":"IF(E26=\"\",\"\",\"Domestic Compact Auto MPG is \"&ROUND(E17,2)&\" with a margin of error of \"&ROUND(E24,2)&\" MPG\")","v":"Domestic Compact Auto MPG is 2.69 with a margin of error of 1.89 MPG"}]
[]
[null,null,null,{"$f":"IF(E26=\"\",\"\",\"We do run a 5% risk that our population difference is not in our interval.\")","v":"We do run a 5% risk that our population difference is not in our interval."}]

{"sheet":"HT Sigma NOT Known, t","index":9,"n_rows":38,"n_cols":10,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
["A recent EPA study compared the highway fuel economy of domestic and imported compact cars"]
[{"$f":"\"A sample of \"&COUNT(A9:A28)&\" domestic compact cars revealed a mean of \"&ROUND(AVERAGE(A9:A28),2)&\" MPG with a standard deviation of \"&ROUND(_xlfn.STDEV.S(A9:A28),2)&\" MPG\"","v":"A sample of 20 domestic compact cars revealed a mean of 33.83 MPG with a standard deviation of 2.33 MPG"}]
[{"$f":"\"A sample of \"&COUNT(B9:B28)&\" imported compact cars revealed a mean of \"&ROUND(AVERAGE(B9:B28),2)&\" MPG with a standard deviation of \"&ROUND(_xlfn.STDEV.S(B9:B28),2)&\" MPG\"","v":"A sample of 20 imported compact cars revealed a mean of 36.52 MPG with a standard deviation of 3.43 MPG"}]
["Samples are independent, Distributions for samples are normal ."]
["\tAt the .05 significance level can the EPA conclude that the MPG is higher on the imported cars?\r\n",null,null,null,null,null," <"]
[]
["Sample 1","Sample 2",null,null,"Sample 1","Sample 2"]
["Domestic MPG","Imported MPG",null,"Car Type","Domestic MPG","Imported MPG",null,"Sample 2 Formulas"]
[35.729999999999997,31.07,null,"Sample Size = n =",null,null,null,{"$f":"IF(F9=\"\",\"\",\" \"&_xlfn.FORMULATEXT(F9))","v":""}]
[35.43,38.71,null,"n -1 =",null,null,null,""]
[34.04,34.369999999999997,null,"Sample Mean = Xbar =",null,null,"MPG",""]
[33.01,37.47,null,"Sample Standard Deviation = s =",null,null,"MPG",""]
[34.81,40.700000000000003,null,"Sample Variance = SVar = s^2 =",null,null,null,""]
[34.97,32.979999999999997,null,"Svar/n = S^2/n =",null,null,null,""]
[28.35,34.76]
[31.87,40.61,null,"Step 1: List Null and Alternative Hypotheses"]
[34.78,35.54,null,"H0 : m1 - m2"]
[31.27,37.78,null,"Ha : m1 - m2"]
[38.229999999999997,32.47]
[31.11,36,null,"Hypothesized Pop Difference"]
[33.83,36.08]
[33.44,31.15,null,"Step 2: Pick Level of Significance = Alpha (Risk that H0 is TRUE, but we Reject it)"]
[34.340000000000003,37.65,null,"Alpha",null,"Risk that we Reject H0, even though it was TRUE (Type I Error)"]
[38.07,44.14]
[33.880000000000003,33.81,null,"Step 3: Sample, Calculate, Draw Picture, Calculate Test Statistic"]
[31.58,37.93,null,"SE",null,null,{"$f":"IF(E26=\"\",\"\",\" \"&_xlfn.FORMULATEXT(E26))","v":""}]
[35.06,40.659999999999997,null,"Test Statistic = t =",null,null,{"$f":"IF(E27=\"\",\"\",\" \"&_xlfn.FORMULATEXT(E27))","v":""},null,null,"# of SD"]
[32.700000000000003,36.49,null,"Degrees of Freedom = df =",null,null,{"$f":"IF(E28=\"\",\"\",\" \"&_xlfn.FORMULATEXT(E28))","v":""}]
[]
[null,null,null,"Step 4: Create Rules for Critical Value and p-value"]
[null,null,null,"If Test Statistic is past our hurdle on the low end, we reject H0 and Accept Ha, Otherwise we fail to reject H0"]
[null,null,null,"Critical Value",null,null,{"$f":"IF(E32=\"\",\"\",\" \"&_xlfn.FORMULATEXT(E32))","v":""}]
[null,null,null,"If p-value is smaller than our Alpha, we reject H0 and accept Ha, otherwise we fail to reject H0."]
[null,null,null,"p-value",null,null,{"$f":"IF(E34=\"\",\"\",\" \"&_xlfn.FORMULATEXT(E34))","v":""}]
[]
[null,null,null,"Step 5: Conclude"]
[null,null,null,{"$f":"IF(E34=\"\",\"\",\"The statistical evidence strongly suggests that the MPG for the import compact cars is greater than for the domestic compact cars.\")","v":""}]
[null,null,null,{"$f":"IF(E34=\"\",\"\",\"The test statistic was well beyond our  critical value and the p-value was much smaller than our alpha and so we reject the H0 and accept the Ha.\")","v":""}]

{"sheet":"HT Sigma NOT Known, t (an)","index":10,"n_rows":54,"n_cols":10,"rows_kept":54,"cut":false,"hidden":false,"merged":[]}
["A recent EPA study compared the highway fuel economy of domestic and imported compact cars"]
[{"$f":"\"A sample of \"&COUNT(A9:A28)&\" domestic compact cars revealed a mean of \"&ROUND(AVERAGE(A9:A28),2)&\" MPG with a standard deviation of \"&ROUND(_xlfn.STDEV.S(A9:A28),2)&\" MPG\"","v":"A sample of 20 domestic compact cars revealed a mean of 33.83 MPG with a standard deviation of 2.33 MPG"}]
[{"$f":"\"A sample of \"&COUNT(B9:B28)&\" imported compact cars revealed a mean of \"&ROUND(AVERAGE(B9:B28),2)&\" MPG with a standard deviation of \"&ROUND(_xlfn.STDEV.S(B9:B28),2)&\" MPG\"","v":"A sample of 20 imported compact cars revealed a mean of 36.52 MPG with a standard deviation of 3.43 MPG"}]
["Samples are independent, Distributions for samples are normal ."]
["\tAt the .05 significance level can the EPA conclude that the MPG is higher on the imported cars?\r\n",null,null,null,null,null," <"]
[]
["Sample 1","Sample 2",null,null,"Sample 1","Sample 2"]
["Domestic MPG","Imported MPG",null,"Car Type","Domestic MPG","Imported MPG",null,"Sample 2 Formulas"]
[35.729999999999997,31.07,null,"Sample Size = n =",{"$f":"COUNT(A9:A28)","v":20},{"$f":"COUNT(B9:B28)","v":20},null,{"$f":"IF(F9=\"\",\"\",\" \"&_xlfn.FORMULATEXT(F9))","v":" =COUNT(B9:B28)"}]
[35.43,38.71,null,"n -1 =",{"$f":"E9-1","v":19},{"$f":"F9-1","v":19},null," =F9-1"]
[34.04,34.369999999999997,null,"Sample Mean = Xbar =",{"$f":"AVERAGE(A9:A28)","v":33.82500000000001},{"$f":"AVERAGE(B9:B28)","v":36.518499999999996},"MPG"," =AVERAGE(B9:B28)"]
[33.01,37.47,null,"Sample Standard Deviation = s =",{"$f":"_xlfn.STDEV.S(A9:A28)","v":2.3337016000111781},{"$f":"_xlfn.STDEV.S(B9:B28)","v":3.4329567967600547},"MPG"," =STDEV.S(B9:B28)"]
[34.81,40.700000000000003,null,"Sample Variance = SVar = s^2 =",{"$f":"E12^2","v":5.4461631578947323},{"$f":"F12^2","v":11.785192368421056},null," =F12^2"]
[34.97,32.979999999999997,null,"Svar/n = S^2/n =",{"$f":"E13/E9","v":0.27230815789473661},{"$f":"F13/F9","v":0.58925961842105279},null," =F13/F9"]
[28.35,34.76]
[31.87,40.61,null,"Step 1: List Null and Alternative Hypotheses"]
[34.78,35.54,null,"H0 : m1 - m2"," >=",{"$f":"$E$20","v":0}]
[31.27,37.78,null,"Ha : m1 - m2"," <",0]
[38.229999999999997,32.47]
[31.11,36,null,"Hypothesized Pop Difference",0]
[33.83,36.08]
[33.44,31.15,null,"Step 2: Pick Level of Significance = Alpha (Risk that H0 is TRUE, but we Reject it)"]
[34.340000000000003,37.65,null,"Alpha",0.05,"Risk that we Reject H0, even though it was TRUE (Type I Error)"]
[38.07,44.14]
[33.880000000000003,33.81,null,"Step 3: Sample, Calculate, Draw Picture, Calculate Test Statistic"]
[31.58,37.93,null,"SE",{"$f":"SQRT(SUM(E14:F14))","v":0.92820675300053135},null,{"$f":"IF(E26=\"\",\"\",\" \"&_xlfn.FORMULATEXT(E26))","v":" =SQRT(SUM(E14:F14))"}]
[35.06,40.659999999999997,null,"Test Statistic = t =",{"$f":"(E11-F11-E20)/E26","v":-2.9018319370042809},null,{"$f":"IF(E27=\"\",\"\",\" \"&_xlfn.FORMULATEXT(E27))","v":" =(E11-F11-E20)/E26"},null,null,"# of SD"]
[32.700000000000003,36.49,null,"Degrees of Freedom = df =",{"$f":"SUM(E14:F14)^2/SUM(E14^2/E10,F14^2/F10)","v":33.470329535142355},null,{"$f":"IF(E28=\"\",\"\",\" \"&_xlfn.FORMULATEXT(E28))","v":" =SUM(E14:F14)^2/SUM(E14^2/E10,F14^2/F10)"}]
[]
[null,null,null,"Step 4: Create Rules for Critical Value and p-value"]
[null,null,null,"If Test Statistic is past our hurdle on the low end, we reject H0 and Accept Ha, Otherwise we fail to reject H0"]
[null,null,null,"Critical Value",{"$f":"_xlfn.T.INV(E23,E28)","v":-1.6923603090303456},null,{"$f":"IF(E32=\"\",\"\",\" \"&_xlfn.FORMULATEXT(E32))","v":" =T.INV(E23,E28)"}]
[null,null,null,"If p-value is smaller than our Alpha, we reject H0 and accept Ha, otherwise we fail to reject H0."]
[null,null,null,"p-value",{"$f":"_xlfn.T.DIST(E27,E28,1)","v":3.2805671569926817E-3},null,{"$f":"IF(E34=\"\",\"\",\" \"&_xlfn.FORMULATEXT(E34))","v":" =T.DIST(E27,E28,1)"}]
[]
[null,null,null,"Step 5: Conclude"]
[null,null,null,{"$f":"IF(E34=\"\",\"\",\"The statistical evidence strongly suggests that the MPG for the import compact cars is greater than for the domestic compact cars.\")","v":"The statistical evidence strongly suggests that the MPG for the import compact cars is greater than for the domestic compact cars."}]
[null,null,null,{"$f":"IF(E34=\"\",\"\",\"The test statistic was well beyond our  critical value and the p-value was much smaller than our alpha and so we reject the H0 and accept the Ha.\")","v":"The test statistic was well beyond our  critical value and the p-value was much smaller than our alpha and so we reject the H0 and accept the Ha."}]
[]
[]
[]
[null,null,null,"t-Test: Two-Sample Assuming Unequal Variances"]
[]
[null,null,null,null,"Domestic MPG","Imported MPG"]
[null,null,null,"Mean",33.82500000000001,36.518499999999996]
[null,null,null,"Variance",5.4461631578947332,11.785192368421056]
[null,null,null,"Observations",20,20]
[null,null,null,"Hypothesized Mean Difference",0]
[null,null,null,"df",33]
[null,null,null,"t Stat",-2.9018319370042809]
[null,null,null,"P(T<=t) one-tail",3.2805671569926817E-3]
[null,null,null,"t Critical one-tail",1.6923603090303456]
[null,null,null,"P(T<=t) two-tail",6.5611343139853635E-3]
[null,null,null,"t Critical two-tail",2.0345152974493397]

{"sheet":"HT & CI Matched Sample, t","index":11,"n_rows":41,"n_cols":8,"rows_kept":41,"cut":false,"hidden":false,"merged":[]}
["Worker","Time (minutes) Making Quad Boomerang Method 1","Time (minutes) Making Quad Boomerang Method 2","Difference in Time\n(M1-M2) (di)"]
[1,12,11,null,null,"At alpha = 0.05, is there a difference in Method 1 and Method 2 for making Quads?"]
[2,11,11.3]
[3,13,10.5,null,null,"Step 1: List Null and Alternative Hypotheses"]
[4,12.2,12,null,null,"H0 : md "]
[5,12,12,null,null,"Ha : md "]
[6,13,13.1]
[7,11.2,10.4,null,null,"Mean of Differences in Population = μd =",null,"Assumes \"No Difference\""]
[8,10.9,10.8,null,null,null,null,"Hypothesized Pop Difference"]
[9,12.5,12]
[10,12.4,11.8,null,null,"Step 2: Pick Level of Significance = Alpha (Risk that H0 is TRUE, but we Reject it)"]
[null,null,null,null,null,"Alpha",null,"Risk that we Reject H0, even though it was TRUE (Type I Error)"]
[null,null,null,null,null,"Alpha/2"]
[]
[null,null,null,null,null,"Step 3: Sample, Calculate, Draw Picture, Calculate Test Statistic"]
[null,null,null,null,null,"Mean of Match Sample Differences = dbar"]
[null,null,null,null,null,"SD of Match Sample Differences = sd"]
[null,null,null,null,null,"Sample Size = n ="]
[null,null,null,null,null,"Degrees of Freedom = n - 1 ="]
[null,null,null,null,null,"SE"]
[null,null,null,null,null,"Test Statistic = t ="]
[]
[null,null,null,null,null,"Step 4: Create Rules for Critical Value and p-value"]
[null,null,null,null,null,"If Test Statistic is past our hurdle on the low end or the upper end, we reject H0 and Accept Ha, Otherwise we fail to reject H0"]
[null,null,null,null,null,"Critical Value"]
[]
[null,null,null,null,null,"If p-value is smaller than our Alpha, we reject H0 and accept Ha, otherwise we fail to reject H0."]
[null,null,null,null,null,"p-value"]
[]
[null,null,null,null,null,"Step 5: Conclude"]
[null,null,null,null,null,{"$f":"IF(G29=\"\",\"\",\"The statistical evidence does not support the conclusion that there is a difference between the two methods for making Quad Boomerangs..\")","v":""}]
[null,null,null,null,null,{"$f":"IF(G29=\"\",\"\",\"The test statistic is not past our critical value and the p-value was bigger than our alpha and so we fail to reject H0.\")","v":""}]
[]
[null,null,null,null,null,"95% Confidence Interval:"]
[null,null,null,null,null,"Margin of Error ="]
[]
[null,null,null,null,null,"Upper Value"]
[null,null,null,null,null,"Lower Value"]
[]
[null,null,null,null,null,"Conclude"]
[null,null,null,null,null,{"$f":"IF(G38=\"\",\"\",\"We are 95% sure that the population difference will be between \"&ROUND(G37,4)&\" and \"&ROUND(G38,4)&\" minutes.\")","v":""}]

{"sheet":"HT & CI Matched Sample, t (an)","index":12,"n_rows":41,"n_cols":8,"rows_kept":41,"cut":false,"hidden":false,"merged":[]}
["Worker","Time (minutes) Making Quad Boomerang Method 1","Time (minutes) Making Quad Boomerang Method 2","Difference in Time\n(M1-M2) (di)"]
[1,12,11,{"$f":"B2-C2","v":1},null,"At alpha = 0.05, is there a difference in Method 1 and Method 2 for making Quads?"]
[2,11,11.3,{"$f":"B3-C3","v":-0.30000000000000071}]
[3,13,10.5,2.5,null,"Step 1: List Null and Alternative Hypotheses"]
[4,12.2,12,0.19999999999999929,null,"H0 : md "," =",{"$f":"$G$8","v":0}]
[5,12,12,0,null,"Ha : md "," <>",0]
[6,13,13.1,-9.9999999999999645E-2]
[7,11.2,10.4,0.79999999999999893,null,"Mean of Differences in Population = μd =",0,"Assumes \"No Difference\""]
[8,10.9,10.8,9.9999999999999645E-2,null,null,null,"Hypothesized Pop Difference"]
[9,12.5,12,0.5]
[10,12.4,11.8,0.59999999999999964,null,"Step 2: Pick Level of Significance = Alpha (Risk that H0 is TRUE, but we Reject it)"]
[null,null,null,null,null,"Alpha",0.05,"Risk that we Reject H0, even though it was TRUE (Type I Error)"]
[null,null,null,null,null,"Alpha/2",{"$f":"G12/2","v":2.5000000000000001E-2}]
[]
["t-Test: Paired Two Sample for Means",null,null,null,null,"Step 3: Sample, Calculate, Draw Picture, Calculate Test Statistic"]
[null,null,null,null,null,"Mean of Match Sample Differences = dbar",{"$f":"AVERAGE(D2:D11)","v":0.52999999999999969}]
[null,"Time (minutes) Making Quad Boomerang Method 1","Time (minutes) Making Quad Boomerang Method 2",null,null,"SD of Match Sample Differences = sd",{"$f":"_xlfn.STDEV.S(D2:D11)","v":0.80560536244491332}]
["Mean",12.020000000000001,11.489999999999998,null,null,"Sample Size = n =",{"$f":"COUNT(D2:D11)","v":10}]
["Variance",0.58844444444444433,0.70988888888888857,null,null,"Degrees of Freedom = n - 1 =",{"$f":"G18-1","v":9}]
["Observations",10,10,null,null,"SE",{"$f":"G17/SQRT(G18)","v":0.25475478405713997}]
["Pearson Correlation",0.50233076753414496,null,null,null,"Test Statistic = t =",{"$f":"(G16-G8)/G20","v":2.0804319807439766}]
["Hypothesized Mean Difference",0]
["df",9,null,null,null,"Step 4: Create Rules for Critical Value and p-value"]
["t Stat",2.0804319807439766,null,null,null,"If Test Statistic is past our hurdle on the low end or the upper end, we reject H0 and Accept Ha, Otherwise we fail to reject H0"]
["P(T<=t) one-tail",3.3609046846371421E-2,null,null,null,"Critical Value",{"$f":"_xlfn.T.INV(1-G13,G19)","v":2.2621571627982049}]
["t Critical one-tail",1.8331129326562374,null,null,null,null,{"$f":"_xlfn.T.INV.2T(G12,G19)","v":2.2621571627982053}]
["P(T<=t) two-tail",6.7218093692742842E-2,null,null,null,"If p-value is smaller than our Alpha, we reject H0 and accept Ha, otherwise we fail to reject H0."]
["t Critical two-tail",2.2621571627982053,null,null,null,"p-value",{"$f":"(1-_xlfn.T.DIST(G21,G19,1))*2","v":6.7218093692742897E-2}]
[null,null,null,null,null,null,{"$f":"_xlfn.T.DIST.2T(G21,G19)","v":6.7218093692742842E-2}]
[null,null,null,null,null,"Step 5: Conclude"]
[null,null,null,null,null,{"$f":"IF(G29=\"\",\"\",\"The statistical evidence does not support the conclusion that there is a difference between the two methods for making Quad Boomerangs..\")","v":"The statistical evidence does not support the conclusion that there is a difference between the two methods for making Quad Boomerangs.."}]
[null,null,null,null,null,{"$f":"IF(G29=\"\",\"\",\"The test statistic is not past our critical value and the p-value was bigger than our alpha and so we fail to reject H0.\")","v":"The test statistic is not past our critical value and the p-value was bigger than our alpha and so we fail to reject H0."}]
[]
[null,null,null,null,null,"95% Confidence Interval:"]
[null,null,null,null,null,"Margin of Error =",{"$f":"G25*G20","v":0.57629535951196909}]
[null,null,null,null,null,null,{"$f":"_xlfn.CONFIDENCE.T(G12,G17,G18)","v":0.5762953595119692}]
[null,null,null,null,null,"Upper Value",{"$f":"G16+G35","v":1.1062953595119689}]
[null,null,null,null,null,"Lower Value",{"$f":"G16-G35","v":-4.6295359511969392E-2}]
[]
[null,null,null,null,null,"Conclude"]
[null,null,null,null,null,{"$f":"IF(G38=\"\",\"\",\"We are 95% sure that the population difference will be between \"&ROUND(G37,4)&\" and \"&ROUND(G38,4)&\" minutes.\")","v":"We are 95% sure that the population difference will be between 1.1063 and -0.0463 minutes."}]

{"sheet":"CRD(1)","index":13,"n_rows":103,"n_cols":20,"rows_kept":103,"cut":false,"hidden":false,"merged":[]}
["1) Rand Function:"]
[null,null,null,"2) Radomly Select with VLOOKUP and SMALL:",null,null,null,null,null,"4) Rand Function:"]
["RAND","Employees Making Boomerangs:",null,null,null,null,null,"3) For Names, Paste Special Values:"]
[{"$f":"RAND()","v":0.70641166528613353},"Annette Caldwell",null,"No.","Boomerang Maker","Method",null,null,null,null,null,null,null,null,null,"5) For Methods, Paste Special Values:"]
[{"$f":"RAND()","v":0.99383457549637499},"Sophia Wise",null,1,{"$f":"VLOOKUP(SMALL($A$4:$B$103,D5),$A$4:$B$103,2,0)","v":"Joel Hansen"},"Method 1",null,"Sophia Wise",null,"RAND","Method"]
[0.41568852058442474,"Florence Ferguson",null,2,"Kelli Sherman","Method 2",null,"Alexandra Moran",null,{"$f":"RAND()","v":7.9111574130994455E-2},"Method 1",null,null,null,null,"Sophia Wise","Method 4",null,{"$f":"P6='CRD(2)'!I2","v":false},{"$f":"Q6='CRD(2)'!J2","v":true}]
[0.4169515317881699,"Jorge Reid",null,3,"Kathy Dean","Method 3",null,"Herbert Garrett",null,{"$f":"RAND()","v":0.47575038527697622},"Method 1",null,null,null,null,"Alexandra Moran","Method 4",null,{"$f":"P7='CRD(2)'!I3","v":true},{"$f":"Q7='CRD(2)'!J3","v":true}]
[0.57310270587138223,"Belinda Ruiz",null,4,"Lora Patrick","Method 4",null,"Sharon Richardson",null,0.9049134705238967,"Method 1",null,null,null,null,"Herbert Garrett","Method 3",null,{"$f":"P8='CRD(2)'!I4","v":true},{"$f":"Q8='CRD(2)'!J4","v":true}]
[0.46053388037032961,"Everett Marsh",null,5,"Denise Farmer","Method 1",null,"Robert Valdez",null,4.4098909154387078E-2,"Method 1",null,null,null,null,"Sharon Richardson","Method 4",null,{"$f":"P9='CRD(2)'!I5","v":true},{"$f":"Q9='CRD(2)'!J5","v":true}]
[7.4934792830164798E-2,"Guy Frazier",null,6,"Marsha Gutierrez","Method 2",null,"Winifred Ortega",null,0.27186128975835633,"Method 1",null,null,null,null,"Robert Valdez","Method 2",null,{"$f":"P10='CRD(2)'!I6","v":true},{"$f":"Q10='CRD(2)'!J6","v":true}]
[0.55741397734103459,"Angel Clayton",null,7,"Van Simmons","Method 3",null,"Carole Sullivan",null,0.45446028015271045,"Method 2",null,null,null,null,"Winifred Ortega","Method 3",null,{"$f":"P11='CRD(2)'!I7","v":true},{"$f":"Q11='CRD(2)'!J7","v":true}]
[0.27415032930757821,"Johnnie Zimmerman",null,8,"Jose Goodman","Method 4",null,"Willard Payne",null,0.20084651390310015,"Method 2",null,null,null,null,"Carole Sullivan","Method 3",null,{"$f":"P12='CRD(2)'!I8","v":true},{"$f":"Q12='CRD(2)'!J8","v":true}]
[0.98286655749244467,"Jenna Rios",null,9,"Paula Wade","Method 1",null,"Irvin Owens",null,2.1157071064851873E-2,"Method 2",null,null,null,null,"Willard Payne","Method 1",null,{"$f":"P13='CRD(2)'!I9","v":true},{"$f":"Q13='CRD(2)'!J9","v":true}]
[0.66582379338653308,"Alvin Mccoy",null,10,"Guy Frazier","Method 2",null,"Constance Henderson",null,0.16594845676288206,"Method 2",null,null,null,null,"Irvin Owens","Method 2",null,{"$f":"P14='CRD(2)'!I10","v":true},{"$f":"Q14='CRD(2)'!J10","v":true}]
[0.37075327049161,"Carole Sullivan",null,11,"Glenn George","Method 3",null,"Jodi Houston",null,0.42748240770856738,"Method 2",null,null,null,null,"Constance Henderson","Method 2",null,{"$f":"P15='CRD(2)'!I11","v":true},{"$f":"Q15='CRD(2)'!J11","v":true}]
[0.35452637338788129,"Winifred Ortega",null,12,"Sylvia Nichols","Method 4",null,"Danny Mullins",null,0.90766598600430859,"Method 3",null,null,null,null,"Jodi Houston","Method 1",null,{"$f":"P16='CRD(2)'!I12","v":true},{"$f":"Q16='CRD(2)'!J12","v":true}]
[0.97659512513063707,"Lucas Ortiz",null,13,"Saul Harmon","Method 1",null,"Jaime Gibson",null,0.5777140343836259,"Method 3",null,null,null,null,"Danny Mullins","Method 4",null,{"$f":"P17='CRD(2)'!I13","v":true},{"$f":"Q17='CRD(2)'!J13","v":true}]
[0.19917661816752363,"Sharon Richardson",null,14,"Traci Myers","Method 2",null,"Arlene Baker",null,0.6265050832024861,"Method 3",null,null,null,null,"Jaime Gibson","Method 2",null,{"$f":"P18='CRD(2)'!I14","v":true},{"$f":"Q18='CRD(2)'!J14","v":true}]
[4.2466113492528823E-2,"Marsha Gutierrez",null,15,"Tracy Chambers","Method 3",null,"Guy Frazier",null,0.73239635587810192,"Method 3",null,null,null,null,"Arlene Baker","Method 3",null,{"$f":"P19='CRD(2)'!I15","v":true},{"$f":"Q19='CRD(2)'!J15","v":true}]
[0.2822241823463193,"Jodi Houston",null,16,"Lamar Hammond","Method 4",null,"Van Simmons",null,1.6774218486885761E-3,"Method 3",null,null,null,null,"Guy Frazier","Method 1",null,{"$f":"P20='CRD(2)'!I16","v":true},{"$f":"Q20='CRD(2)'!J16","v":true}]
[0.18738951128688597,"Ora Kim",null,17,"Cheryl Ford","Method 1",null,"Floyd Erickson",null,0.47081832947461488,"Method 4",null,null,null,null,"Van Simmons","Method 1",null,{"$f":"P21='CRD(2)'!I17","v":true},{"$f":"Q21='CRD(2)'!J17","v":true}]
[0.81540510177127923,"Loren Freeman",null,18,"Ora Kim","Method 2",null,"Denise Farmer",null,0.42626424951167319,"Method 4",null,null,null,null,"Floyd Erickson","Method 1",null,{"$f":"P22='CRD(2)'!I18","v":true},{"$f":"Q22='CRD(2)'!J18","v":true}]
[0.96266878321558602,"Danny Mullins",null,19,"Herbert Garrett","Method 3",null,"Reginald Montgomery",null,0.57224887095492383,"Method 4",null,null,null,null,"Denise Farmer","Method 4",null,{"$f":"P23='CRD(2)'!I19","v":true},{"$f":"Q23='CRD(2)'!J19","v":true}]
[0.75954005946955216,"Jared Young",null,20,"Sharon Richardson","Method 4",null,"Edwin Watkins",null,0.34512117231264761,"Method 4",null,null,null,null,"Reginald Montgomery","Method 3",null,{"$f":"P24='CRD(2)'!I20","v":true},{"$f":"Q24='CRD(2)'!J20","v":true}]
[0.57434013705590248,"Sylvester Hodges",null,null,null,null,null,null,null,0.24990360030914172,"Method 4",null,null,null,null,"Edwin Watkins","Method 2",null,{"$f":"P25='CRD(2)'!I21","v":true},{"$f":"Q25='CRD(2)'!J21","v":true}]
[0.87400474577408827,"Daniel Watson"]
[0.73052078058069336,"Nathan Beck"]
[0.16655310111681221,"Lamar Hammond"]
[0.27591545386976091,"Tommie Turner"]
[0.8161790121073067,"Garrett King"]
[0.81477750045883157,"Bradford Boone"]
[0.55428457362312411,"Julian Quinn"]
[0.85467373371849165,"Phyllis Waters"]
[0.67431470713521557,"Carlton Matthews"]
[0.66893259223969515,"Kimberly Palmer"]
[0.79708575332294174,"Arlene Baker"]
[6.4245935212516314E-2,"Jose Goodman"]
[0.52813436714422857,"Floyd Erickson"]
[0.5201551377426562,"Faith Salazar"]
[2.7681380760491092E-2,"Kathy Dean"]
[0.92697164656643993,"Ernestine Weaver"]
[0.64553129508540719,"Judy Mckenzie"]
[0.58823475894409316,"Nina Alvarez"]
[0.69726679435017602,"Irvin Owens"]
[0.43804151890318754,"Bernard Day"]
[0.33743937913453548,"Todd Rowe"]
[0.52165002440616148,"Abraham Park"]
[0.7824113175204872,"Lorraine Wilson"]
[9.4769593437640021E-2,"Sylvia Nichols"]
[0.40748962828315727,"Moses Cooper"]
[0.10782446834347592,"Saul Harmon"]
[0.22014872191273938,"Jaime Gibson"]
[0.51035495950924004,"Malcolm Jefferson"]
[3.0242562252819627E-2,"Denise Farmer"]
[0.61123321822193277,"Jasmine Manning"]
[0.21090295906020273,"Chester Munoz"]
[0.46808545096645071,"Jeanette Maldonado"]
[0.22597666938204442,"Bernice Castillo"]
[0.37404081722038329,"Claire Christensen"]
[0.92542376103968116,"Doris Luna"]
[0.79830168619544561,"Vivian Hubbard"]
[0.31050889669438231,"Harvey Grant"]
[0.17506422760568241,"Cheryl Ford"]
[0.29818509062325327,"Brandy Andrews"]
[0.41609599416373733,"Kerry Herrera"]
[0.2678327002140336,"Shelly Fuller"]
[0.94843331987782409,"Louis Schwartz"]
[8.0395932039534546E-2,"Glenn George"]
[{"$f":"RAND()","v":0.49826771501543843},"Stacey Saunders"]
[0.64652409952585754,"Leroy Oliver"]
[0.65656118009583186,"Johanna Miles"]
[0.70977820891271248,"Felix Cain"]
[0.7204872248541847,"Stella Mccarthy"]
[0.62648976306042625,"Alice Harris"]
[3.0058349887298386E-2,"Lora Patrick"]
[0.4864351460221541,"Marcella Morton"]
[0.26016293084840225,"Inez Stone"]
[0.89798068859659663,"Trevor Phelps"]
[0.6306308800777547,"Gene Lindsey"]
[0.7576291867652426,"Jacob Ingram"]
[0.60643539290505521,"Rene Bishop"]
[0.72037838891352057,"Robert Valdez"]
[0.76267311911959101,"Georgia Olson"]
[5.8929054976006423E-2,"Van Simmons"]
[0.67847660254946041,"Reginald Montgomery"]
[0.5000541713640817,"Edwin Watkins"]
[0.33453506416258305,"Miriam Ramos"]
[0.60506899120803403,"Alexandra Moran"]
[0.15535982068744025,"Tracy Chambers"]
[1.4102951009099085E-2,"Joel Hansen"]
[0.19179144093252143,"Herbert Garrett"]
[0.46215443067854456,"Julio Peterson"]
[0.32267169092376158,"Matthew West"]
[0.38072254885370271,"Sadie Hall"]
[0.1313891465460385,"Traci Myers"]
[0.25508809492122464,"Constance Henderson"]
[0.42464237616254485,"Thelma Howard"]
[2.3609679230880309E-2,"Kelli Sherman"]
[0.77330789644965781,"Willard Payne"]
[7.1073153526705402E-2,"Paula Wade"]
[0.35116020136196879,"Lynne Griffin"]
[0.54533527149498606,"Colin Austin"]
[0.42031578611310949,"Carrie Baldwin"]

{"sheet":"CRD(2)","index":14,"n_rows":101,"n_cols":17,"rows_kept":101,"cut":false,"hidden":false,"merged":[]}
["Employees Making\nBoomerangs:",null,"From List 0f 100, randomly\nselect 20 Workers ==>",null,"Workers",null,"Randomly Assign\nManufacturing Method ==>",null,"Workers","Method",null,"Time and\nrecord data ==>>",null,"Pop 1","Pop 2","Pop 3","Pop 4"]
["Annette Caldwell",null,null,null,"Sophia Wise",null,null,null,".       ","Method 4",null,null,null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4"]
["Sophia Wise",null,null,null,"Alexandra Moran",null,null,null,"Alexandra Moran","Method 4",null,null,null,"Method 1","Method 2","Method 3","Method 4"]
["Florence Ferguson",null,null,null,"Herbert Garrett",null,null,null,"Herbert Garrett","Method 3",null,null,null,12.56,11.87,15.57,12.94]
["Jorge Reid",null,null,null,"Sharon Richardson",null,null,null,"Sharon Richardson","Method 4",null,null,null,15.92,12.94,10.64,12.01]
["Belinda Ruiz",null,null,null,"Robert Valdez",null,null,null,"Robert Valdez","Method 2",null,null,null,10.42,11.23,14.05,10.210000000000001]
["Everett Marsh",null,null,null,"Winifred Ortega",null,null,null,"Winifred Ortega","Method 3",null,null,null,14.41,15.97,13.08,10.18]
["Guy Frazier",null,null,null,"Carole Sullivan",null,null,null,"Carole Sullivan","Method 3",null,null,null,10.32,17.14,16.71,11.21]
["Angel Clayton",null,null,null,"Willard Payne",null,null,null,"Willard Payne","Method 1"]
["Johnnie Zimmerman",null,null,null,"Irvin Owens",null,null,null,"Irvin Owens","Method 2"]
["Jenna Rios",null,null,null,"Constance Henderson",null,null,null,"Constance Henderson","Method 2"]
["Alvin Mccoy",null,null,null,"Jodi Houston",null,null,null,"Jodi Houston","Method 1"]
["Carole Sullivan",null,null,null,"Danny Mullins",null,null,null,"Danny Mullins","Method 4"]
["Winifred Ortega",null,null,null,"Jaime Gibson",null,null,null,"Jaime Gibson","Method 2"]
["Lucas Ortiz",null,null,null,"Arlene Baker",null,null,null,"Arlene Baker","Method 3"]
["Sharon Richardson",null,null,null,"Guy Frazier",null,null,null,"Guy Frazier","Method 1"]
["Marsha Gutierrez",null,null,null,"Van Simmons",null,null,null,"Van Simmons","Method 1"]
["Jodi Houston",null,null,null,"Floyd Erickson",null,null,null,"Floyd Erickson","Method 1"]
["Ora Kim",null,null,null,"Denise Farmer",null,null,null,"Denise Farmer","Method 4"]
["Loren Freeman",null,null,null,"Reginald Montgomery",null,null,null,"Reginald Montgomery","Method 3"]
["Danny Mullins",null,null,null,"Edwin Watkins",null,null,null,"Edwin Watkins","Method 2"]
["Jared Young"]
["Sylvester Hodges"]
["Daniel Watson"]
["Nathan Beck"]
["Lamar Hammond"]
["Tommie Turner"]
["Garrett King"]
["Bradford Boone"]
["Julian Quinn"]
["Phyllis Waters"]
["Carlton Matthews"]
["Kimberly Palmer"]
["Arlene Baker"]
["Jose Goodman"]
["Floyd Erickson"]
["Faith Salazar"]
["Kathy Dean"]
["Ernestine Weaver",null,"60 more in list below"]
["Judy Mckenzie",null,"<\n<\n<\n<"]
["Nina Alvarez"]
["Irvin Owens"]
["Bernard Day"]
["Todd Rowe"]
["Abraham Park"]
["Lorraine Wilson"]
["Sylvia Nichols"]
["Moses Cooper"]
["Saul Harmon"]
["Jaime Gibson"]
["Malcolm Jefferson"]
["Denise Farmer"]
["Jasmine Manning"]
["Chester Munoz"]
["Jeanette Maldonado"]
["Bernice Castillo"]
["Claire Christensen"]
["Doris Luna"]
["Vivian Hubbard"]
["Harvey Grant"]
["Cheryl Ford"]
["Brandy Andrews"]
["Kerry Herrera"]
["Shelly Fuller"]
["Louis Schwartz"]
["Glenn George"]
["Stacey Saunders"]
["Leroy Oliver"]
["Johanna Miles"]
["Felix Cain"]
["Stella Mccarthy"]
["Alice Harris"]
["Lora Patrick"]
["Marcella Morton"]
["Inez Stone"]
["Trevor Phelps"]
["Gene Lindsey"]
["Jacob Ingram"]
["Rene Bishop"]
["Robert Valdez"]
["Georgia Olson"]
["Van Simmons"]
["Reginald Montgomery"]
["Edwin Watkins"]
["Miriam Ramos"]
["Alexandra Moran"]
["Tracy Chambers"]
["Joel Hansen"]
["Herbert Garrett"]
["Julio Peterson"]
["Matthew West"]
["Sadie Hall"]
["Traci Myers"]
["Constance Henderson"]
["Thelma Howard"]
["Kelli Sherman"]
["Willard Payne"]
["Paula Wade"]
["Lynne Griffin"]
["Colin Austin"]
["Carrie Baldwin"]

{"sheet":"ANOVA-Long","index":15,"n_rows":41,"n_cols":11,"rows_kept":41,"cut":false,"hidden":false,"merged":[]}
["H0 : µ1 = µ2 = µ3 = µ4"]
["Ha = Not all population means are the same (at leat two are different)"]
["Decision Rule: p-value < alpha, Reject H0 & Acceot Ha or Test Ststistic F > Critical F, Reject H0 & Accept Ha"]
[]
[null,"Population 1","Population 2","Population 3","Population 4",null,"Calculations for Total Variance for All Observations ="]
[null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4",null,null,"Population 1","Population 2","Population 3","Population 4"]
[null,"Method 1","Method 2","Method 3","Method 4",null,null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4"]
[null,12.56,11.87,15.57,12.94,null,null,"Method 1","Method 2","Method 3","Method 4"]
[null,15.92,12.94,10.64,12.01]
[null,10.42,11.23,14.05,10.210000000000001]
[null,14.41,15.97,13.08,10.18]
[null,10.32,17.14,16.71,11.21]
["Sample Size = n ="]
["Sample Mean = Xbar ="]
["Sample Variance = s2 =",null,null,null,null,null,"Sum of Squares Total = SST ="]
[null,null,null,null,null,null,"dfT =",null," **Observations - # Samples"]
["Grand Over All Count = nT ="]
["Grand Over All Sample Mean = XbarG =",null,null,null,null,null,"Calculations for Variance Between Treatments ="]
["# Treatments = k =",null,null,null,null,null,null,"Population 1","Population 2","Population 3","Population 4"]
[null,null,null,null,null,null,null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4"]
["Estimate of Variance Bewteen Treatments = MSTR = SSTR/dfTR",null,null,null,null,null,null,"Method 1","Method 2","Method 3","Method 4"]
["Estimate of Variance Within Treatments = MSE = SSE/dfE",null,null,null,null,null,"Deviations Square"]
["F Test Statistic = MSTR/MSE =",null,null,null,null,null,"Total Deviations Squared"]
["Alpha ="]
["p-value =",null,null,null,null,null,"Sum of Squares of Treatments = SSTR =",null,"Sum of Squares for Treatments = SSTR"]
["F Critical",null,null,null,null,null,"dfTR =",null," **Observations - # Samples"]
[]
["Because the F Calculated Test Statistic is not past our F Critical, We Fail To Reject H0. "]
["It seems reasonable to assume that the pop means are the same.",null,null,null,null,null,"Calculations for Variance Within Treatments ="]
["It seems reasonable to assume that there is no significant difference",null,null,null,null,null,null,"Population 1","Population 2","Population 3","Population 4"]
[null,null,null,null,null,null,null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4"]
[null,null,null,null,null,null,null,"Method 1","Method 2","Method 3","Method 4"]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,"Total Deviations Squared"]
[]
[null,null,null,null,null,null,"Sum of Squares Error = SSE ="]
[null,null,null,null,null,null,"dfE =",null," **Observations - # Samples"]

{"sheet":"ANOVA-Long (an)","index":16,"n_rows":41,"n_cols":11,"rows_kept":41,"cut":false,"hidden":false,"merged":[]}
["H0 : µ1 = µ2 = µ3 = µ4"]
["Ha = Not all population means are the same (at leat two are different)"]
["Decision Rule: p-value < alpha, Reject H0 & Acceot Ha or Test Ststistic F > Critical F, Reject H0 & Accept Ha"]
[]
[null,"Population 1","Population 2","Population 3","Population 4",null,"Calculations for Total Variance for All Observations ="]
[null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4",null,null,"Population 1","Population 2","Population 3","Population 4"]
[null,"Method 1","Method 2","Method 3","Method 4",null,null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4"]
[null,12.56,11.87,15.57,12.94,null,null,"Method 1","Method 2","Method 3","Method 4"]
[null,15.92,12.94,10.64,12.01,null,null,{"$f":"(B8-$B$18)^2","v":0.16728100000000201},{"$f":"(C8-$B$18)^2","v":1.2078010000000083},6.765200999999986,8.4100000000020107E-4]
[null,10.42,11.23,14.05,10.210000000000001,null,null,{"$f":"(B9-$B$18)^2","v":8.7084009999999825},8.4100000000020107E-4,5.424241000000011,0.91968100000000608]
[null,14.41,15.97,13.08,10.18,null,null,6.4974010000000151,{"$f":"(C10-$B$18)^2","v":3.0241210000000089},1.1685609999999951,7.6120810000000114]
[null,10.32,17.14,16.71,11.21,null,null,2.0764809999999918,9.0060009999999853,1.2320999999999357E-2,7.7785210000000182]
["Sample Size = n =",{"$f":"COUNT(B8:B12)","v":5},{"$f":"COUNT(C8:C12)","v":5},5,5,null,null,7.0172010000000142,17.39724099999998,13.995080999999985,3.0940810000000076]
["Sample Mean = Xbar =",{"$f":"AVERAGE(B8:B12)","v":12.726000000000001},{"$f":"AVERAGE(C8:C12)","v":13.830000000000002},14.010000000000002,11.309999999999999]
["Sample Variance = s2 =",{"$f":"_xlfn.VAR.S(B8:B12)","v":6.0428799999999967},{"$f":"_xlfn.VAR.S(C8:C12)","v":6.7323499999999967},5.4867499999999438,1.4109499999999993,null,"Sum of Squares Total = SST =",{"$f":"SUM(H9:K13)","v":101.87338},{"$f":"H25+H40","v":101.87338000000005}]
[null,null,null,null,null,null,"dfT =",{"$f":"B17-1","v":19}," **Observations - # Samples"]
["Grand Over All Count = nT =",{"$f":"COUNT(B8:E12)","v":20},null,null,null,null,null,{"$f":"_xlfn.VAR.S(B8:E12)","v":5.3617568421051676},{"$f":"H15/H16","v":5.3617568421052626}]
["Grand Over All Sample Mean = XbarG =",{"$f":"AVERAGE(B8:E12)","v":12.969000000000003},{"$f":"SUMPRODUCT(B14:E14,B13:E13)/SUM(B13:E13)","v":12.968999999999999},null,null,null,"Calculations for Variance Between Treatments ="]
["# Treatments = k =",{"$f":"COUNTA(B7:E7)","v":4},null,null,null,null,null,"Population 1","Population 2","Population 3","Population 4"]
[null,null,null,null,null,null,null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4"]
["Estimate of Variance Bewteen Treatments = MSTR = SSTR/dfTR",{"$f":"H25/H26","v":7.7272200000000169},null,null,null,null,null,"Method 1","Method 2","Method 3","Method 4"]
["Estimate of Variance Within Treatments = MSE = SSE/dfE",{"$f":"H40/H41","v":4.9182325000000002},null,null,null,null,"Deviations Square",{"$f":"(B14-$B$18)^2","v":5.9049000000001024E-2},{"$f":"(C14-$B$18)^2","v":0.74132099999999812},1.083680999999997,2.7522810000000142]
["F Test Statistic = MSTR/MSE =",{"$f":"B21/B22","v":1.5711375987206819},null,null,null,null,"Total Deviations Squared",{"$f":"H22*B13","v":0.29524500000000514},{"$f":"I22*C13","v":3.7066049999999908},5.4184049999999848,13.761405000000071]
["Alpha =",0.05]
["p-value =",{"$f":"_xlfn.F.DIST.RT(B23,H26,H41)","v":0.23529584506194443},null,null,null,null,"Sum of Squares of Treatments = SSTR =",{"$f":"SUM(H23:K23)","v":23.181660000000051},"Sum of Squares for Treatments = SSTR"]
["F Critical",{"$f":"_xlfn.F.INV.RT(B24,H26,H41)","v":3.2388715174535854},null,null,null,null,"dfTR =",{"$f":"B19-1","v":3}," **Observations - # Samples"]
[]
["Because the F Calculated Test Statistic is not past our F Critical, We Fail To Reject H0. "]
["It seems reasonable to assume that the pop means are the same.",null,null,null,null,null,"Calculations for Variance Within Treatments ="]
["It seems reasonable to assume that there is no significant difference",null,null,null,null,null,null,"Population 1","Population 2","Population 3","Population 4"]
[null,null,null,null,null,null,null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4"]
[null,null,null,null,null,null,null,"Method 1","Method 2","Method 3","Method 4"]
[null,null,null,null,null,null,null,{"$f":"(B8-$B$14)^2","v":2.7556000000000122E-2},{"$f":"(C8-$C$14)^2","v":3.8416000000000103},{"$f":"(D8-$D$14)^2","v":2.4335999999999962},{"$f":"(E8-$E$14)^2","v":2.6569000000000025}]
[null,null,null,null,null,null,null,{"$f":"(B9-$B$14)^2","v":10.201635999999993},{"$f":"(C9-$C$14)^2","v":0.79210000000000413},{"$f":"(D9-$D$14)^2","v":11.356900000000007},{"$f":"(E9-$E$14)^2","v":0.49000000000000149}]
[null,null,null,null,null,null,null,5.3176360000000047,6.7600000000000078,1.5999999999999318E-3,1.2099999999999953]
[null,null,null,null,null,null,null,2.8358559999999975,4.5795999999999948,0.86490000000000278,1.2768999999999977]
[null,null,null,null,null,null,null,5.7888360000000025,10.956099999999992,7.2899999999999965,9.9999999999995735E-3]
[null,null,null,null,null,null,"Total Deviations Squared",{"$f":"SUM(H33:H37)","v":24.171519999999997},{"$f":"SUM(I33:I37)","v":26.929400000000008},21.947000000000003,5.643799999999997]
[]
[null,null,null,null,null,null,"Sum of Squares Error = SSE =",{"$f":"SUM(H38:K38)","v":78.691720000000004}]
[null,null,null,null,null,null,"dfE =",{"$f":"B17-B19","v":16}," **Observations - # Samples"]

{"sheet":"ANOVA-Short","index":17,"n_rows":38,"n_cols":5,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
["H0 : µ1 = µ2 = µ3 = µ4"]
["Ha = Not all population means are the same (at least two are different)"]
["Decision Rule: p-value < alpha, Reject H0 & Accept Ha or Test Statistic F > Critical F, Reject H0 & Accept Ha, otherwise we fail to Reject H0"]
[]
[null,"Population 1","Population 2","Population 3","Population 4"]
[null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4"]
[null,"Method 1","Method 2","Method 3","Method 4"]
[null,12.56,11.87,15.57,12.94]
[null,15.92,12.94,10.64,12.01]
[null,10.42,11.23,14.05,10.210000000000001]
[null,14.41,15.97,13.08,10.18]
[null,10.32,17.14,16.71,11.21]
["Sample Size = n =",{"$f":"COUNT(B8:B12)","v":5},{"$f":"COUNT(C8:C12)","v":5},5,5]
["Sample Mean = Xbar =",{"$f":"AVERAGE(B8:B12)","v":12.726000000000001},{"$f":"AVERAGE(C8:C12)","v":13.830000000000002},14.010000000000002,11.309999999999999]
["Sample Variance = s2 =",{"$f":"_xlfn.VAR.S(B8:B12)","v":6.0428799999999967},{"$f":"_xlfn.VAR.S(C8:C12)","v":6.7323499999999967},5.4867499999999438,1.4109499999999993]
[]
["Grand Over All Count = nT =",{"$f":"COUNT(B8:E12)","v":20}]
["Grand Over All Sample Mean = XbarG =",{"$f":"AVERAGE(B8:E12)","v":12.969000000000003},"Check:",{"$f":"SUMPRODUCT(B14:E14,B13:E13)/SUM(B13:E13)","v":12.968999999999999}]
["# Treatments = k =",{"$f":"COUNTA(B7:E7)","v":4}]
["Calculations for Total Variance for All Observations ="]
["Sum of Squares Total = SST =",null,"Check:"]
["dfT ="]
["Calculations for Variance Between Treatments ="]
["Sum of Squares of Treatments = SSTR ="]
["dfTR ="]
["Estimate of Variance Between Treatments = MSTR = SSTR/dfTR"]
["Calculations for Variance Within Treatments ="]
["Sum of Squares Error = SSE =",null,"Check:"]
["dfE ="]
["Estimate of Variance Within Treatments = MSE = SSE/dfE"]
["F Test Statistic = MSTR/MSE ="]
["Alpha ="]
["p-value ="]
["F Critical"]
[]
["Because the F Calculated Test Statistic is not past our F Critical, We Fail To Reject H0. "]
["It seems reasonable to assume that the pop means are the same."]
["It seems reasonable to assume that there is no significant difference"]

{"sheet":"ANOVA-Short (an)","index":18,"n_rows":38,"n_cols":5,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
["H0 : µ1 = µ2 = µ3 = µ4"]
["Ha = Not all population means are the same (at least two are different)"]
["Decision Rule: p-value < alpha, Reject H0 & Accept Ha or Test Statistic F > Critical F, Reject H0 & Accept Ha, otherwise we fail to Reject H0"]
[]
[null,"Population 1","Population 2","Population 3","Population 4"]
[null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4"]
[null,"Method 1","Method 2","Method 3","Method 4"]
[null,12.56,11.87,15.57,12.94]
[null,15.92,12.94,10.64,12.01]
[null,10.42,11.23,14.05,10.210000000000001]
[null,14.41,15.97,13.08,10.18]
[null,10.32,17.14,16.71,11.21]
["Sample Size = n =",{"$f":"COUNT(B8:B12)","v":5},{"$f":"COUNT(C8:C12)","v":5},5,5]
["Sample Mean = Xbar =",{"$f":"AVERAGE(B8:B12)","v":12.726000000000001},{"$f":"AVERAGE(C8:C12)","v":13.830000000000002},14.010000000000002,11.309999999999999]
["Sample Variance = s2 =",{"$f":"_xlfn.VAR.S(B8:B12)","v":6.0428799999999967},{"$f":"_xlfn.VAR.S(C8:C12)","v":6.7323499999999967},5.4867499999999438,1.4109499999999993]
[]
["Grand Over All Count = nT =",{"$f":"COUNT(B8:E12)","v":20}]
["Grand Over All Sample Mean = XbarG =",{"$f":"AVERAGE(B8:E12)","v":12.969000000000003},"Check:",{"$f":"SUMPRODUCT(B14:E14,B13:E13)/SUM(B13:E13)","v":12.968999999999999}]
["# Treatments = k =",{"$f":"COUNTA(B7:E7)","v":4}]
["Calculations for Total Variance for All Observations ="]
["Sum of Squares Total = SST =",{"$f":"SUMPRODUCT((B8:E12-B18)^2)","v":101.87338},"Check:",{"$f":"B24+B28","v":101.87338000000007},{"$f":"_xlfn.VAR.P(B8:E12)*B17","v":101.87337999999799}]
["dfT =",{"$f":"B17-1","v":19}]
["Calculations for Variance Between Treatments ="]
["Sum of Squares of Treatments = SSTR =",{"$f":"SUMPRODUCT((B14:E14-B18)^2,B13:E13)","v":23.181660000000051}]
["dfTR =",{"$f":"B19-1","v":3}]
["Estimate of Variance Between Treatments = MSTR = SSTR/dfTR",{"$f":"B24/B25","v":7.7272200000000169}]
["Calculations for Variance Within Treatments ="]
["Sum of Squares Error = SSE =",{"$f":"SUMPRODUCT((B8:E12-B14:E14)^2)","v":78.691720000000018},"Check:",{"$f":"SUMPRODUCT(B15:E15,B13:E13-1)","v":78.691719999999748}]
["dfE =",{"$f":"B17-B19","v":16}]
["Estimate of Variance Within Treatments = MSE = SSE/dfE",{"$f":"B28/B29","v":4.9182325000000011}]
["F Test Statistic = MSTR/MSE =",{"$f":"B26/B30","v":1.5711375987206817}]
["Alpha =",0.05]
["p-value =",{"$f":"_xlfn.F.DIST.RT(B31,B25,B29)","v":0.23529584506194448}]
["F Critical",{"$f":"_xlfn.F.INV.RT(B32,B25,B29)","v":3.2388715174535854}]
[]
["Because the F Calculated Test Statistic is not past our F Critical, We Fail To Reject H0. "]
["It seems reasonable to assume that the pop means are the same."]
["It seems reasonable to assume that there is no significant difference"]

{"sheet":"Formulas","index":19,"n_rows":34,"n_cols":5,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
[]
[]
[]
[]
[null,"Population 1","Population 2","Population 3","Population 4"]
[null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4"]
[null,"Method 1","Method 2","Method 3","Method 4"]
[null,12.56,11.87,15.57,12.94]
[null,15.92,12.94,10.64,12.01]
[null,10.42,11.23,14.05,10.210000000000001]
[null,14.41,15.97,13.08,10.18]
[null,10.32,17.14,16.71,11.21]
["Sample Size = n =",{"$f":"COUNT(B8:B12)","v":5},5,5,5]
["Sample Mean = Xbar =",{"$f":"AVERAGE(B8:B12)","v":12.726000000000001},13.830000000000002,14.010000000000002,11.309999999999999]
["Sample Variance = s2 =",{"$f":"_xlfn.VAR.S(B8:B12)","v":6.0428799999999967},6.7323499999999967,5.4867499999999438,1.4109499999999993]
[]
["Grand Over All Count = nT =",{"$f":"COUNT(B8:E12)","v":20}]
["Grand Over All Sample Mean = XbarG =",{"$f":"AVERAGE(B8:E12)","v":12.969000000000003},"Check:",{"$f":"SUMPRODUCT(B13:E13,B14:E14)/SUM(B13:E13)","v":12.968999999999999}]
["# Treatments = k =",{"$f":"COUNTA(B7:E7)","v":4}]
["Calculations for Total Variance for All Observations ="]
["Sum of Squares Total = SST =",{"$f":"SUMPRODUCT((B8:E12-B18)^2)","v":101.87338},"Check:",{"$f":"B24+B28","v":101.8733799999998},{"$f":"_xlfn.VAR.P(B8:E12)*B17","v":101.87337999999799}]
["dfT =",{"$f":"B17-1","v":19}]
["Calculations for Variance Between Treatments ="]
["Sum of Squares of Treatments = SSTR =",{"$f":"SUMPRODUCT((B14:E14-B18)^2,B13:E13)","v":23.181660000000051}]
["dfTR =",{"$f":"B19-1","v":3}]
["Estimate of Variance Between Treatments = MSTR = SSTR/dfTR",{"$f":"B24/B25","v":7.7272200000000169}]
["Calculations for Variance Within Treatments ="]
["Sum of Squares Error = SSE =",{"$f":"SUMPRODUCT(B15:E15,B13:E13-1)","v":78.691719999999748},"Check:",{"$f":"SUMPRODUCT((B8:E12-B14:E14)^2)","v":78.691720000000018}]
["dfE =",{"$f":"B17-B19","v":16}]
["Estimate of Variance Within Treatments = MSE = SSE/dfE",{"$f":"B28/B29","v":4.9182324999999842}]
["F Test Statistic = MSTR/MSE =",{"$f":"B26/B30","v":1.571137598720687}]
["Alpha =",0.05]
["p-value =",{"$f":"_xlfn.F.DIST.RT(B31,B25,B29)","v":0.23529584506194329}]
["F Critical",{"$f":"_xlfn.F.INV.RT(B32,B25,B29)","v":3.2388715174535854}]

{"sheet":"ANOVA-Data Analysis","index":20,"n_rows":12,"n_cols":8,"rows_kept":12,"cut":false,"hidden":false,"merged":[]}
["H0 : µ1 = µ2 = µ3 = µ4"]
["Ha = Not all population means are the same (at least two are different)"]
["Decision Rule: p-value < alpha, Reject H0 & Accept Ha or Test Statistic F > Critical F, Reject H0 & Accept Ha, otherwise we fail to Reject H0"]
[]
[null,"Population 1","Population 2","Population 3","Population 4",null,null,"Because our p-value is larger than alpha, We Fail To Reject H0. It seems reasonable to assume that the pop means are the same."]
[null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4",null,null,"It seems reasonable to assume that there is no significant difference"]
[null,"Method 1","Method 2","Method 3","Method 4"]
[null,12.56,11.87,15.57,12.94]
[null,15.92,12.94,10.64,12.01]
[null,10.42,11.23,14.05,10.210000000000001]
[null,14.41,15.97,13.08,10.18]
[null,10.32,17.14,16.71,11.21]

{"sheet":"ANOVA-Data Analysis (an)","index":21,"n_rows":34,"n_cols":7,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
["H0 : µ1 = µ2 = µ3 = µ4"]
["Ha = Not all population means are the same (at least two are different)"]
["Decision Rule: p-value < alpha, Reject H0 & Accept Ha or Test Statistic F > Critical F, Reject H0 & Accept Ha, otherwise we fail to Reject H0"]
[]
[null,"Population 1","Population 2","Population 3","Population 4"]
[null,"Treatment 1","Treatment 2","Treatment 3","Treatment 4"]
[null,"Method 1","Method 2","Method 3","Method 4"]
[null,12.56,11.87,15.57,12.94]
[null,15.92,12.94,10.64,12.01]
[null,10.42,11.23,14.05,10.210000000000001]
[null,14.41,15.97,13.08,10.18]
[null,10.32,17.14,16.71,11.21]
[]
[]
["Anova: Single Factor"]
[]
["SUMMARY"]
["Groups","Count","Sum","Average","Variance"]
["Method 1",5,63.63,12.726000000000001,6.0428799999999967]
["Method 2",5,69.150000000000006,13.830000000000002,6.7323499999999967]
["Method 3",5,70.050000000000011,14.010000000000002,5.4867499999999438]
["Method 4",5,56.55,11.309999999999999,1.4109499999999993]
[]
[]
["ANOVA"]
["Source of Variation","SS","df","MS","F","P-value","F crit"]
["Between Groups",23.181659999999994,3,7.7272199999999982,1.5711375987206782,0.23529584506194526,3.2388715174535854]
["Within Groups",78.691720000000004,16,4.9182325000000002]
[]
["Total",101.87338,19]
[]
[]
["Because our p-value is larger than alpha, We Fail To Reject H0. It seems reasonable to assume that the pop means are the same."]
["It seems reasonable to assume that there is no significant difference"]

{"sheet":"ANOVA(2)","index":22,"n_rows":58,"n_cols":10,"rows_kept":58,"cut":false,"hidden":false,"merged":[]}
["Students rate a professor either: Excellent, Good, Par, Below Par"]
["Ratings = Factor = Independent Variable"]
["Ratings = Treatments = Populations"]
["Student's grades are matched up with Rating"]
["Class grades = Response Variable"]
["Students = Experimental Units"]
[]
["Null and Alternative Hypothesis:"]
["H0 : µ1 = µ2 = … = µk"]
["Ha : Not all population means are equal"]
["\"at least two mean are not equal\""]
["Alpha =",0.01]
[]
[null,"Class Grades"]
[null,"Excellent","Good","Par","Below Par"]
[null,94,75,70,68]
[null,90,68,73,70]
[null,85,77,76,72]
[null,80,83,78,65]
[null,null,88,80,74]
[null,null,null,68,65]
[null,null,null,65]
["Sample Size = n =",{"$f":"COUNT(B16:B22)","v":4},5,7,6,null,null,null,"Inference about pairs of Treatment Means"]
["Sample Mean = Xbar =",{"$f":"AVERAGE(B16:B22)","v":87.25},78.2,72.857142857142861,69]
["Sample Variance = S2 =",{"$f":"_xlfn.VAR.S(B16:B22)","v":36.916666666666664},58.7,30.142857142857139,13.6,null,null,null,"Alpha",0.05]
["Sample SD = s =",{"$f":"SQRT(B25)","v":6.0759087111860612},7.6615925237511817,5.4902511001644667,3.687817782917155,null,null,null,"Alpha/2",{"$f":"J25/2","v":2.5000000000000001E-2}]
["Sample Variance = S2 =",{"$f":"SUMPRODUCT((B16:B19-B24)^2)/(B23-1)","v":36.916666666666664},{"$f":"SUMPRODUCT((C16:C20-C24)^2)/(C23-1)","v":58.7},{"$f":"SUMPRODUCT((D16:D22-D24)^2)/(D23-1)","v":30.142857142857139},{"$f":"SUMPRODUCT((E16:E21-E24)^2)/(E23-1)","v":13.6},null,null,null,"t",{"$f":"_xlfn.T.INV(1-J26,C35)","v":2.1009220402410378}]
[null,null,null,null,null,null,null,null,"XbarE - XbarBP",{"$f":"B24-E24","v":18.25}]
["# Treatments = k =",{"$f":"COUNTA(B15:E15)","v":4},null,null,null,null,null,null,"Margin of Error = t*SQRT(MSE*(1/n+1/n2))"]
["Grand Overall Sample Size = nT =",{"$f":"COUNT(B16:E22)","v":22},null,null,null,null,null,null,null,{"$f":"J27*SQRT(D35*(1/B23+1/E23))","v":7.7930968503563376}]
["Grand Overall Sample Mean = XbarG =",{"$f":"AVERAGE(B16:E22)","v":75.63636363636364},{"$f":"SUMPRODUCT(B24:E24,B23:E23)/SUM(B23:E23)","v":75.63636363636364},null,null,null,null,null,"Lower Limit",{"$f":"J28-J30","v":10.456903149643662}]
[null,null,null,"2 estimates of variance",null,null,null,null,"Upper Limit",{"$f":"J28+J30","v":26.043096850356338}]
["Source of Variation","Sum of Squares","Degrees of Freedom","Mean Square","F","p-value","F Critical",null,"Since 0 is not in interval, it seems reasonable that there is a difference."]
["Treatments (Between Group)",{"$f":"SUMPRODUCT(B23:E23,(B24:E24-B31)^2)","v":890.68376623376616},{"$f":"B29-1","v":3},{"$f":"B34/C34","v":296.8945887445887},{"$f":"D34/D35","v":8.9906433016855161},{"$f":"_xlfn.F.DIST.RT(E34,C34,C35)","v":7.4276889848416238E-4},{"$f":"_xlfn.F.INV.RT(B12,C34,C35)","v":5.0918895204140124}]
["Error (Within Group)",{"$f":"SUMPRODUCT(B25:E25,B23:E23-1)","v":594.40714285714284},{"$f":"B30-B29","v":18},33.022619047619045]
["Total",{"$f":"SUMPRODUCT(--ISNUMBER(B16:E22),(B16:E22-B31)^2)","v":1485.090909090909},{"$f":"B30-1","v":21},70.718614718614717]
[]
[null,null,null,{"$f":"_xlfn.VAR.S(B16:E22)","v":70.718614718614845}]
[null,{"$f":"SUMPRODUCT(--ISNUMBER(B16:E22),(B16:E22-B24:E24)^2)","v":594.40714285714284}]
[null,{"$f":"B34+B35","v":1485.090909090909}]
[]
[]
["Anova: Single Factor"]
[]
["SUMMARY"]
["Groups","Count","Sum","Average","Variance"]
["Excellent",4,349,87.25,36.916666666666664]
["Good",5,391,78.2,58.7]
["Par",7,510,72.857142857142861,30.142857142857139]
["Below Par",6,414,69,13.6]
[]
[]
["ANOVA"]
["Source of Variation","SS","df","MS","F","P-value","F crit"]
["Between Groups",890.68376623376616,3,296.8945887445887,8.9906433016855161,7.4276889848416238E-4,5.0918895204140124]
["Within Groups",594.40714285714284,18,33.022619047619045]
[]
["Total",1485.090909090909,21]

{"sheet":"ANOVA(3)","index":23,"n_rows":38,"n_cols":14,"rows_kept":38,"cut":false,"hidden":false,"merged":[]}
["3 Paints advertised as having the same dry time (until ready to apply second coat)"]
["We want to check Manufacturer's claim"]
["5 random samples of each paint are taken (5 cans of each paint)"]
["Dry times in minutes"]
[null,"Group 1","Group 2","Group 3"]
[null,"Population 1","Population 2","Population 3"]
[null,"Treatment 1","Treatment 2","Treatment 3"]
[null,"Paint 1\nTime (Mins)","Paint 2\nTime (Mins)","Paint 3\nTime (Mins)",null,"Source of Variation","Names","Sum of Squares","Degrees of Freedom","Names","Mean Square","F","p-value","F Critical"]
[null,131,147,153,null,"Treatment (Between Groups)","SSTR",{"$f":"SUMPRODUCT(B14:D14,(B15:D15-B18)^2)","v":270.53333333333364},{"$f":"B20-1","v":2},"MSTR",{"$f":"H9/I9","v":135.26666666666682},{"$f":"K9/K10","v":2.9794419970631458},{"$f":"_xlfn.F.DIST.RT(L9,I9,I10)","v":8.9004385386150145E-2},{"$f":"_xlfn.F.INV.RT(G20,I9,I10)","v":3.8852938346523942}]
[null,140,136,145,null,"Error (Within Groups)","SSE",{"$f":"SUMPRODUCT(B16:D16,B14:D14-1)","v":544.79999999999995},{"$f":"B19-B20","v":12},"MSE",{"$f":"H10/I10","v":45.4}]
[null,138,145,138,null,"Total Variation","SSTR",{"$f":"SUMPRODUCT((B9:D13-B18)^2)","v":815.33333333333348},{"$f":"B19-1","v":14},"VAR.S",{"$f":"H11/I11","v":58.238095238095248}]
[null,129,148,143]
[null,144,133,155,null,null,null,"Check:",null,null,"Check:"]
["Count = n =",{"$f":"COUNT(B9:B13)","v":5},{"$f":"COUNT(C9:C13)","v":5},{"$f":"COUNT(D9:D13)","v":5},null,null,null,{"$f":"SUMPRODUCT((B9:D13-B15:D15)^2)","v":544.79999999999995}]
["Mean = Xbar =",{"$f":"AVERAGE(B9:B13)","v":136.4},{"$f":"AVERAGE(C9:C13)","v":141.80000000000001},{"$f":"AVERAGE(D9:D13)","v":146.80000000000001},null,null,null,{"$f":"H9+H10","v":815.3333333333336},null,null,{"$f":"_xlfn.VAR.S(B9:D13)","v":58.238095238095248}]
["Sample Var = s2 =",{"$f":"SUMPRODUCT((B9:B13-B15)^2)/(B14-1)","v":39.299999999999997},{"$f":"SUMPRODUCT((C9:C13-C15)^2)/(C14-1)","v":46.699999999999996},{"$f":"SUMPRODUCT((D9:D13-D15)^2)/(D14-1)","v":50.199999999999996}]
[null,null,null,null,null,"Is Mean Dry time the same for each type of paint?"]
["Grand Overall Sample Mean =",{"$f":"AVERAGE(B9:D13)","v":141.66666666666666},{"$f":"SUMPRODUCT(B15:D15,B14:D14)/SUM(B14:D14)","v":141.66666666666666},null,null,"H0 : m1 = m2 = m3 = m4"]
["Grand Overall Count =",{"$f":"COUNT(B9:D13)","v":15},null,null,null,"Ha : All means are not the same"]
["# of Treantments/Populations = k =",{"$f":"COUNTA(B8:D8)","v":3},null,null,null,"Alpha =",0.05]
[null,null,null,null,null,"Because p-value greater than alpha, we fail to reject. The sample evidemnce does not support the conclusion that there is a difference in dry times."]
[null,3]
[]
[null,null,null,null,null,"Anova: Single Factor"]
[]
[null,null,null,null,null,"SUMMARY"]
[null,null,null,null,null,"Groups","Count","Sum","Average","Variance"]
[null,null,null,null,null,"Paint 1",5,682,136.4,39.299999999999997]
[null,null,null,null,null,"Paint 2",5,709,141.80000000000001,46.699999999999996]
[null,null,null,null,null,"Paint 3",5,734,146.80000000000001,50.199999999999996]
[]
[]
[null,null,null,null,null,"ANOVA"]
[null,null,null,null,null,"Source of Variation","SS","df","MS","F","P-value","F crit"]
[null,null,null,null,null,"Between Groups",270.53333333333353,2,135.26666666666677,2.9794419970631445,8.9004385386150145E-2,3.8852938346523942]
[null,null,null,null,null,"Within Groups",544.79999999999995,12,45.4]
[]
[null,null,null,null,null,"Total",815.33333333333348,14]