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{"sheet":"Topics","index":0,"n_rows":9,"n_cols":2,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
["Topic","Sheet Link"]
["HT-z-lower",{"$f":"A2","v":"HT-z-lower"}]
["HT-z-Two-Tail","HT-z-Two-Tail"]
["Summary NORM Functions","Summary NORM Functions"]
["HT-t-upper","HT-t-upper"]
["HT-t-lower","HT-t-lower"]
["HT-t-Two-Tail","HT-t-Two-Tail"]
["Summary T Functions","Summary T Functions"]
["Proportions","Proportions"]

{"sheet":"Detailed Topics","index":1,"n_rows":43,"n_cols":18,"rows_kept":43,"cut":false,"hidden":false,"merged":[]}
["Video54:","Excel 2013 Statistical Analysis #54: 1 Tail Left Mean Hypothesis Z Test: P-value & Critical Value"]
["Number","Topic In Video and minute mark in Video.","Time In Video",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Text"]
[{"$f":"ROWS(A3:A$3)","v":1},{"$f":"TRIM(REPLACE(R3,1,SEARCH(\")\",R3)+1,\"\"))","v":"Example of 1 tail test on the left (lower end) for mean catchup bottle weight when consumer group suspects that mean weight is below advertised amount, using critical value and p-value. See the Excel functions: COUNT, AVERAGE, ROUND, NORM.S.DIST and NORM.S.INV"},{"$f":"TRIM(LEFT(R3,SEARCH(\")\",R3)))","v":"(00:10)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(00:10) Example of 1 tail test on the left (lower end) for mean catchup bottle weight when consumer group suspects that mean weight is below advertised amount, using critical value and p-value. See the Excel functions: COUNT, AVERAGE, ROUND, NORM.S.DIST and NORM.S.INV"]
[]
["Video55:","Excel 2013 Statistical Analysis #55: 2 Tail Z Score Mean Hypothesis Testing P-value Critical Value "]
["Number","Topic In Video and minute mark in Video.","Time In Video",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Text"]
[{"$f":"ROWS(A$7:A7)","v":1},{"$f":"TRIM(REPLACE(R7,1,SEARCH(\")\",R7)+1,\"\"))","v":"Example of 2 tail test on the left (lower end) for mean catchup bottle weight when manager of bottle filling machine needs to check if the machine is filling accurately, using critical value and p-value. See the Excel functions: COUNT, AVERAGE, ROUND, NORM.S.DIST and NORM.S.INV"},{"$f":"TRIM(LEFT(R7,SEARCH(\")\",R7)))","v":"(00:10)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(00:10) Example of 2 tail test on the left (lower end) for mean catchup bottle weight when manager of bottle filling machine needs to check if the machine is filling accurately, using critical value and p-value. See the Excel functions: COUNT, AVERAGE, ROUND, NORM.S.DIST and NORM.S.INV"]
[]
["Video56:","Excel 2013 Statistical Analysis #56: NORM.S.DIST = p-value, NORM.S.INV = Critical Value Sigma Known"]
["Number","Topic In Video and minute mark in Video.","Time In Video",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Text"]
[{"$f":"ROWS(A$11:A11)","v":1},{"$f":"TRIM(REPLACE(R11,1,SEARCH(\")\",R11)+1,\"\"))","v":"Upper Tail Test: NORM.S.DIST for p-value, NORM.S.INV for Critical Value Sigma Known"},{"$f":"TRIM(LEFT(R11,SEARCH(\")\",R11)))","v":"(00:11)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(00:11) Upper Tail Test: NORM.S.DIST for p-value, NORM.S.INV for Critical Value Sigma Known"]
[{"$f":"ROWS(A$11:A12)","v":2},{"$f":"TRIM(REPLACE(R12,1,SEARCH(\")\",R12)+1,\"\"))","v":"Lower Tail Test: NORM.S.DIST for p-value, NORM.S.INV for Critical Value Sigma Known"},{"$f":"TRIM(LEFT(R12,SEARCH(\")\",R12)))","v":"(03:38)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(03:38) Lower Tail Test: NORM.S.DIST for p-value, NORM.S.INV for Critical Value Sigma Known"]
[{"$f":"ROWS(A$11:A13)","v":3},"Two Tail Test: NORM.S.DIST for p-value, NORM.S.INV for Critical Value Sigma Known","(05:38)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(05:38) Two Tail Test: NORM.S.DIST for p-value, NORM.S.INV for Critical Value Sigma Known"]
[]
["Video57:","Excel 2013 Statistical Analysis #57: 1 Tail Right Mean Hypothesis T Test P-value & Critical Value"]
["Number","Topic In Video and minute mark in Video.","Time In Video",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Text"]
[{"$f":"ROWS(A$17:A17)","v":1},{"$f":"TRIM(REPLACE(R17,1,SEARCH(\")\",R17)+1,\"\"))","v":"Sigma Not Known, T-Distribution, Hypothesis Testing on the upper end. Manufacturing Fuse Example. See COUNT, AVERAGE and STDEV.S functions. See T.DIST function for calculating p-value and T.INV for calculating Critical t value."},{"$f":"TRIM(LEFT(R17,SEARCH(\")\",R17)))","v":"(00:10)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(00:10) Sigma Not Known, T-Distribution, Hypothesis Testing on the upper end. Manufacturing Fuse Example. See COUNT, AVERAGE and STDEV.S functions. See T.DIST function for calculating p-value and T.INV for calculating Critical t value."]
[]
[]
["Video58:","Excel 2013 Statistical Analysis #58: 1 Tail Left T Score Mean Hypothesis Test P-value Critical Value"]
["Number","Topic In Video and minute mark in Video.","Time In Video",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Text"]
[{"$f":"ROWS(A$22:A22)","v":1},{"$f":"TRIM(REPLACE(R22,1,SEARCH(\")\",R22)+1,\"\"))","v":"Sigma Not Known, T-Distribution, Hypothesis Testing on the upper end. Construction Company Example. See COUNT, AVERAGE and STDEV.S functions. See T.DIST and T.DIST.2T functions for calculating p-value and T.INV and T.INV.2T functions for calculating Critical t value."},{"$f":"TRIM(LEFT(R22,SEARCH(\")\",R22)))","v":"(00:10)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(00:10) Sigma Not Known, T-Distribution, Hypothesis Testing on the upper end. Construction Company Example. See COUNT, AVERAGE and STDEV.S functions. See T.DIST and T.DIST.2T functions for calculating p-value and T.INV and T.INV.2T functions for calculating Critical t value."]
[]
[]
["Video59:","Excel 2013 Statistical Analysis #59: 2 Tail Mean Hypothesis T Test: P-value & Critical Value"]
["Number","Topic In Video and minute mark in Video.","Time In Video",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Text"]
[{"$f":"ROWS(A$27:A27)","v":1},{"$f":"TRIM(REPLACE(R27,1,SEARCH(\")\",R27)+1,\"\"))","v":"Sigma Not Known, T-Distribution, Hypothesis Testing for a two tail test. Seattle Auto Price Example. See COUNT, AVERAGE and STDEV.S functions. See T.DIST function for calculating p-value and T.INV for calculating Critical t value."},{"$f":"TRIM(LEFT(R27,SEARCH(\")\",R27)))","v":"(00:10)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(00:10) Sigma Not Known, T-Distribution, Hypothesis Testing for a two tail test. Seattle Auto Price Example. See COUNT, AVERAGE and STDEV.S functions. See T.DIST function for calculating p-value and T.INV for calculating Critical t value."]
[]
["Video60:","Excel 2013 Statistical Analysis #60: T.DIST, T.DIST.RT, T.DIST.2T, T.INV, T.INV.2T functions"]
["Number","Topic In Video and minute mark in Video.","Time In Video",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Text"]
[{"$f":"ROWS(A$31:A31)","v":1},{"$f":"TRIM(REPLACE(R31,1,SEARCH(\")\",R31)+1,\"\"))","v":"Upper Tail (Right) Test to calculate p-value and Critical Value for Hypothesis Test using T.DIST & T.DIST.RT functions for P-value and T.INV function for Critical Value. Also degrees of freedom, Standard Error and the Test Statistic."},{"$f":"TRIM(LEFT(R31,SEARCH(\")\",R31)))","v":"(00:29)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(00:29) Upper Tail (Right) Test to calculate p-value and Critical Value for Hypothesis Test using T.DIST & T.DIST.RT functions for P-value and T.INV function for Critical Value. Also degrees of freedom, Standard Error and the Test Statistic."]
[{"$f":"ROWS(A$31:A32)","v":2},{"$f":"TRIM(REPLACE(R32,1,SEARCH(\")\",R32)+1,\"\"))","v":"Lower Tail (Left) Test to calculate p-value and Critical Value for Hypothesis Test using T.DIST function for P-value and T.INV function for Critical Value."},{"$f":"TRIM(LEFT(R32,SEARCH(\")\",R32)))","v":"(04:32)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(04:32) Lower Tail (Left) Test to calculate p-value and Critical Value for Hypothesis Test using T.DIST function for P-value and T.INV function for Critical Value."]
[{"$f":"ROWS(A$31:A33)","v":3},"Two Tail Test to calculate p-value and Critical Value for Hypothesis Test using T.DIST & T.DIST.2T functions for P-value and T.INV & T.DIST.2T for Critical Value.","(06:20)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(06:20) Two Tail Test to calculate p-value and Critical Value for Hypothesis Test using T.DIST & T.DIST.2T functions for P-value and T.INV & T.DIST.2T for Critical Value."]
[]
["Video61:","Excel 2013 Statistical Analysis #60: T.DIST, T.DIST.RT, T.DIST.2T, T.INV, T.INV.2T functions"]
["Number","Topic In Video and minute mark in Video.","Time In Video",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Text"]
[{"$f":"ROWS(A$37:A37)","v":1},{"$f":"TRIM(REPLACE(R37,1,SEARCH(\")\",R37)+1,\"\"))","v":"Hypothesis Test for Proportions using p-value or Critical Value. Example: Researcher who was skeptical of reported proportion of the number students know when the presidential election is; Test to see if there is significantly more than 15% of the students who know when the presidential election will be held."},{"$f":"TRIM(LEFT(R37,SEARCH(\")\",R37)))","v":"(00:11)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(00:11) Hypothesis Test for Proportions using p-value or Critical Value. Example: Researcher who was skeptical of reported proportion of the number students know when the presidential election is; Test to see if there is significantly more than 15% of the students who know when the presidential election will be held."]
[{"$f":"ROWS(A$37:A38)","v":2},{"$f":"TRIM(REPLACE(R38,1,SEARCH(\")\",R38)+1,\"\"))","v":"Point of view and Goal and set up Null and Alternative Hypothesis"},{"$f":"TRIM(LEFT(R38,SEARCH(\")\",R38)))","v":"(02:25)"},null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(02:25) Point of view and Goal and set up Null and Alternative Hypothesis"]
[{"$f":"ROWS(A$37:A39)","v":3},"See COUNTIF function to calculate sample proportion.","(04:20)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(04:20) See COUNTIF function to calculate sample proportion."]
[{"$f":"ROWS(A$37:A40)","v":4},"Calculate Standard Error","(05:37)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(05:37) Calculate Standard Error"]
[{"$f":"ROWS(A$37:A41)","v":5},"Calculate Z Test Statistic","(06:30)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(06:30) Calculate Z Test Statistic"]
[{"$f":"ROWS(A$37:A42)","v":6},"See the functions NORM.S.DIST to calculate p-value from a z-score.","(07:11)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(07:11) See the functions NORM.S.DIST to calculate p-value from a z-score."]
[{"$f":"ROWS(A$37:A43)","v":7},"See NORM.S.INV to calculate the Critical value from the alpha probability of 0.01.","(07:55)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"(07:55) See NORM.S.INV to calculate the Critical value from the alpha probability of 0.01."]

{"sheet":"HT-z-upper (an)","index":2,"n_rows":56,"n_cols":16,"rows_kept":56,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting (Original Statement) H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"A statement from an official report said that Realtors make $85,000 a year (national mean). Researcher thinks that Realtors in the Des Moines area have a mean annual salary of more than 85,000 a year. At alpha = .05, sigma = $12,549, n = 36 and sample mean = $88,595, can we conclude that realtors in the Des Moines area make more than $85,000?"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,".","Point of view:","Researcher who believes that Des Moines realtors have an annual mean greater than $85,000"]
[null,".","Considering:","Population of Des Moines Realtors"]
[null,".","Goal:","Run Hypothesis test to provide statistical evidence to support the claim that Des Moines"]
[null,{"$f":"IF(B18=\"\",\"\",\".\")","v":"."},null,"Realtors have an annual mean salary of more than $85,000. Mew > 85000 >>> 1 tail right"]
["Sample Salaries",null,"Step 1: List H0 and Ha","H0 : μ "," <=",{"$f":"D26","v":85000}]
[98356,null,null,"Ha : μ "," >",{"$f":"D26","v":85000}]
[120491.99999999935]
[119398,null,"Step 2: Select Alpha","Alpha =",0.05,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[92682,null,null,null,null,"At alpha = 0.05, 5% risk of rejecting H0 even though it was true, if we reject Mew <= $85,000, about 5 out of 100 times we will be incorrect."]
[113284,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[79398,null,"Hypothesized Mean = μ0 =",85000]
[82503,null,"Sigma = s =",12549]
[81485,null,"Sample SD = s","NA"]
[84083,null,"Test Statistic To Use:","z",null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":"Because Sigma Known"}]
[76384,null,"sample size = n",{"$f":"COUNT(A21:A56)","v":36}]
[86539,null,"Sample Mean = Xbar",{"$f":"AVERAGE(A21:A56)","v":88594.999999999971},null," =AVERAGE(values)"]
[69894,null,"Alpha = a =",{"$f":"E23","v":0.05}]
[67810,null,"Type of Test","One Tail To Right"]
[84219,null,"SE",{"$f":"D27/SQRT(D30)","v":2091.5},null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":" =Sigma/SQRT(n)"},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[90242,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic = z ="},{"$f":"(D31-D26)/D34","v":1.718862060721956},null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[104294]
[86642,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[85646,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[73286,null,"p-value One Tail To Right",{"$f":"1-_xlfn.NORM.S.DIST(D35,1)","v":4.2819745911792384E-2},null,null," =1-NORM.S.DIST(z,1)",null,"Probability of getting Test Statistic or higher"]
[65074]
[77829,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[106881,null,"Rejection Rule:","Test Statistic >= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[83221,null,"Critical Value One Tail To Right",{"$f":"_xlfn.NORM.S.INV(1-D32)","v":1.6448536269514715},null,null," =NORM.S.INV(1-alpha)",null,"This is the hurdle Point"]
[88483]
[80998]
[84734,null,"Step 5: Write Conclusion"]
[126949,".","Because the p-value of 0.043 <= alpha of 0.05, we reject H0 and accept Ha."]
[64085,".","Because the test statistic of 1.72 >= critical value of 1.645, we reject H0 and accept Ha."]
[81469,".","The statistical evidence suggests that the mean annual salary for realtors in Des Moines is"]
[85769,{"$f":"IF(B49=\"\",\"\",\".\")","v":"."},"greater than the national mean."]
[98864,".","At an alpha of 0.05, our sample mean of $88,595 provides statistically significant evidence that"]
[92132,{"$f":"IF(B51=\"\",\"\",\".\")","v":"."},"the mean annual salary for realtors in Des Moines is greater than the national mean."]
[65025,".","We do run a 5% risk of a Type 1 Error that we might say that the mean annual salary for",null,null,null,null,null,null,"False Positive: Reject H0 when it is true."]
[101594,{"$f":"IF(B53=\"\",\"\",\".\")","v":"."},"realtors in Des Moines is greater than $85,00, when it is not greater than $85,000."]
[91250]
[98426]

{"sheet":"HT-z-lower","index":3,"n_rows":120,"n_cols":16,"rows_kept":120,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting (Original Statement) H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"A bottle of \"Yummy Red Catsup\" is labeled as having 16 oz. of catsup. A consumers group in the Green Valley area believes that the bottles are filled with less than 16 oz and asks a government agency to investigate the underfilling. At the 0.05 significance level, can the government agency conclude that the bottle is being underfilled in the Green Valley area? (From the companies data they estimate the population standard deviation to be 0.5 oz.)"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,null,"Point of view:","Consumer group and government agency are concerned about underfilling and label accuracy."]
[null,null,"Considering:","Population of catsup bottles in the Green River area."]
[null,null,"Goal:","Run Hypothesis test to provide statistical evidence to support the claim that the bottles are"]
[null,null,null,"being underfilled.",null," <<<<<<< === One Tail to the Left"]
["oz. per Bottle",null,"Step 1: List H0 and Ha","H0 : μ "]
[16.579999999999998,null,null,"Ha : μ "]
[15.78]
[15.83,null,"Step 2: Select Alpha","Alpha =",null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[16.559999999999999]
[15.24,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[15.44,null,"Hypothesized Mean = μ0 ="]
[16.239999999999998,null,"Sigma = s ="]
[15.7,null,"Sample SD = s"]
[16.11,null,"Test Statistic To Use:",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":""}]
[15.77,null,"sample size = n"]
[16.399999999999999,null,"Sample Mean = Xbar",null,null," =AVERAGE(values)"]
[15.7,null,"Alpha = a ="]
[16.239999999999998,null,"Type of Test"]
[16.27,null,"SE",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":""},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[16.079999999999998,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic =  ="},null,null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[16.190000000000001]
[15.86,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[15.53,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[15.01,null,"p-value One Tail To Left",null,null," =NORM.S.DIST(z,1)",null,null,"Probability of getting Test Statistic or lower"]
[15.39]
[15.53,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[15.3,null,"Rejection Rule:","Test Statistic <= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[16.23,null,"Critical Value One Tail To Left",null,null," =NORM.S.INV(alpha)",null,null,"This is the hurdle Point"]
[16.14]
[16.75]
[15.77,null,"Step 5: Write Conclusion"]
[15.43,null,"Because our p-value of .21 is bigger than our alpha of .05, we Fail To Reject H0."]
[17.05,null,"Because our tests statistic of -0.8 is bigger than our critical value of -1.645, we Fail To Reject H0."]
[15.31,null,"The sample evidence suggests that the mean amount of catsup in the \"Yummy Red Catsup\""]
[16.89,null,"bottles is not less than 16 oz."]
[15.95,null,"At an alpha of 0.05 the sample mean of 15.96 oz. does not provide statistically significant"]
[16.559999999999999,null,"evidence to suggest that the bottles are being underfilled in the Green Valley area."]
[15.83,null,"We do run the Beta Risk (Type 2 Error) of Failing to accept the Alternative (underfilling),"]
[16.28,null,"when the H0 was false. Not accept Ha, when it is true.",null,null,null,null,null,null,"False Negative: Not selecting Ha, when it is true."]
[16.21]
[15.98]
[15.13]
[16.100000000000001]
[15.43]
[16.690000000000001]
[15.99]
[16.059999999999999]
[16.010000000000002]
[15.34]
[16.25]
[16.05]
[16.13]
[15.72]
[15.63]
[16.190000000000001]
[15.63]
[15.87]
[16.309999999999999]
[16.27]
[15.78]
[15.72]
[16.309999999999999]
[16.73]
[16.46]
[16.18]
[15.17]
[16.2]
[16.97]
[15.62]
[15.27]
[15.49]
[16.63]
[15.33]
[15.42]
[15.83]
[15.28]
[16.32]
[17.12]
[15.66]
[15.07]
[16.03]
[16.04]
[16.440000000000001]
[16.41]
[15.55]
[15.87]
[15.23]
[15.59]
[15.14]
[16.260000000000002]
[16.11]
[16.86]
[15.92]
[15.53]
[16.18]
[15.85]
[16.29]
[15.7]
[16.25]
[15.1]
[15.89]
[15.77]
[15.87]
[16.13]
[17.079999999999998]

{"sheet":"HT-z-lower (an)","index":4,"n_rows":120,"n_cols":16,"rows_kept":120,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting (Original Statement) H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"A bottle of \"Yummy Red Catsup\" is labeled as having 16 oz. of catsup. A consumers group in the Green Valley area believes that the bottles are filled with less than 16 oz and asks a government agency to investigate the underfilling. At the 0.05 significance level, can the government agency conclude that the bottle is being underfilled in the Green River area? (From the companies data they estimate the population standard deviation to be 0.5 oz.)"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,".","Point of view:","Consumer group and government agency are concerned about underfilling and label accuracy."]
[null,".","Considering:","Population of catsup bottles in the Green River area."]
[null,".","Goal:","Run Hypothesis test to provide statistical evidence to support the claim that the bottles are"]
[null,{"$f":"IF(B18=\"\",\"\",\".\")","v":"."},null,"being underfilled.",null," <<<<<<< === One Tail to the Left"]
["oz. per Bottle",null,"Step 1: List H0 and Ha","H0 : μ "," >=",{"$f":"$D$26","v":16},"oz."]
[16.579999999999998,null,null,"Ha : μ "," <",16,"oz."]
[15.78]
[15.83,null,"Step 2: Select Alpha","Alpha =",0.05,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[16.559999999999999]
[15.24,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[15.44,null,"Hypothesized Mean = μ0 =",16]
[16.239999999999998,null,"Sigma = s =",0.5]
[15.7,null,"Sample SD = s","NA"]
[16.11,null,"Test Statistic To Use:","z",null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":"Because Sigma Known"}]
[15.77,null,"sample size = n",{"$f":"COUNT($A$21:$A$120)","v":100}]
[16.399999999999999,null,"Sample Mean = Xbar",{"$f":"ROUND(AVERAGE($A$21:$A$120),2)","v":15.96},null," =AVERAGE(values)"]
[15.7,null,"Alpha = a =",{"$f":"E23","v":0.05}]
[16.239999999999998,null,"Type of Test","One Tail To Left"]
[16.27,null,"SE",{"$f":"D27/SQRT(D30)","v":0.05},null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":" =Sigma/SQRT(n)"},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[16.079999999999998,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic = z ="},{"$f":"(D31-D26)/D34","v":-0.79999999999998295},null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[16.190000000000001]
[15.86,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[15.53,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[15.01,null,"p-value One Tail To Left",{"$f":"_xlfn.NORM.S.DIST(D35,1)","v":0.21185539858340163},null," =NORM.S.DIST(z,1)",null,null,"Probability of getting Test Statistic or lower"]
[15.39]
[15.53,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[15.3,null,"Rejection Rule:","Test Statistic <= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[16.23,null,"Critical Value One Tail To Left",{"$f":"_xlfn.NORM.S.INV(D32)","v":-1.6448536269514726},null," =NORM.S.INV(alpha)",null,null,"This is the hurdle Point"]
[16.14]
[16.75]
[15.77,null,"Step 5: Write Conclusion"]
[15.43,".","Because our p-value of .21 is bigger than our alpha of .05, we Fail To Reject H0."]
[17.05,".","Because our tests statistic of -0.8 is bigger than our critical value of -1.645, we Fail To Reject H0."]
[15.31,".","The sample evidence suggests that the mean amount of catsup in the \"Yummy Red Catsup\""]
[16.89,{"$f":"IF(B49=\"\",\"\",\".\")","v":"."},"bottles is not less than 16 oz."]
[15.95,".","At an alpha of 0.05 the sample mean of 15.96 oz. does not provide statistically significant"]
[16.559999999999999,{"$f":"IF(B51=\"\",\"\",\".\")","v":"."},"evidence to suggest that the bottles are being underfilled in the Green Valley area."]
[15.83,".","We do run the Beta Risk (Type 2 Error) of Failing to accept the Alternative (underfilling),"]
[16.28,{"$f":"IF(B53=\"\",\"\",\".\")","v":"."},"when the H0 was false. Not accept Ha, when it is true.",null,null,null,null,null,null,"False Negative: Not selecting Ha, when it is true."]
[16.21]
[15.98]
[15.13]
[16.100000000000001]
[15.43]
[16.690000000000001]
[15.99]
[16.059999999999999]
[16.010000000000002]
[15.34]
[16.25]
[16.05]
[16.13]
[15.72]
[15.63]
[16.190000000000001]
[15.63]
[15.87]
[16.309999999999999]
[16.27]
[15.78]
[15.72]
[16.309999999999999]
[16.73]
[16.46]
[16.18]
[15.17]
[16.2]
[16.97]
[15.62]
[15.27]
[15.49]
[16.63]
[15.33]
[15.42]
[15.83]
[15.28]
[16.32]
[17.12]
[15.66]
[15.07]
[16.03]
[16.04]
[16.440000000000001]
[16.41]
[15.55]
[15.87]
[15.23]
[15.59]
[15.14]
[16.260000000000002]
[16.11]
[16.86]
[15.92]
[15.53]
[16.18]
[15.85]
[16.29]
[15.7]
[16.25]
[15.1]
[15.89]
[15.77]
[15.87]
[16.13]
[17.079999999999998]

{"sheet":"HT-z-Two-Tail","index":5,"n_rows":56,"n_cols":16,"rows_kept":56,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting (Original Statement) H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"A bottle of \"Yummy Red Catsup\" is labeled as having 16 oz. of catsup. The bottle filling factory wants to make sure the filling machine is filling accurately. They do not want to fill too little and make customers unhappy, and they do not want to fill too much and thus decrease profits. At the alpha level of 0.05 is the process out of control? (From the companies data they estimate the population standard deviation to be 0.5 oz.)"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,null,"Point of view:","Manufacturer wants to make sure that machine is filling accurately, not too much, not too little."]
[null,null,"Considering:","Population of all possible bottles that could come off filling line."]
[null,null,"Goal:","Run Hypothesis test to provide statistical evidence to show whether the machine is filling"]
[null,null,null,"accurately, yes, or no.",null,null,"Two Tail"]
["oz. per Bottle",null,"Step 1: List H0 and Ha","H0 : μ "]
[15.25,null,null,"Ha : μ "]
[15.03]
[16.07,null,"Step 2: Select Alpha","Alpha =",null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[16.260000000000002]
[16.22,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[15.49,null,"Hypothesized Mean = μ0 ="]
[15.41,null,"Sigma = s ="]
[17.522227666665689,null,"Sample SD = s"]
[15.5,null,"Test Statistic To Use:",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":""}]
[16,null,"sample size = n"]
[16,null,"Sample Mean = Xbar",null,null," =AVERAGE(values)"]
[16.66,null,"Alpha = a ="]
[15.74,null,"Type of Test"]
[14.97,null,"SE",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":""},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[15.6,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic =  ="},null,null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[16.13]
[15.96,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[17.21,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[16.64,null,"p-value Two Tail",null,null," =NORM.S.DIST(lower z,1)*2",null,null,"Probability of getting less than - Test Statistic or greatern than + Test Statistic"]
[15.65,null,null,null,null," =(1-NORM.S.DIST(upper z,1))*2"]
[16.07,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[16.62,null,"Rejection Rule:"," =-Critical Value  < Test Statistic < +Critical Value, Fail to Reject H0 , otherwsie Reject H0 and accept Ha "]
[16.59,null,"Lower Critial Value",null,null," =NORM.S.INV(alpha/2)",null,null,"This is the hurdle Point"]
[15.7,null,"Upper Critial Value",null,null," =-NORM.S.INV(alpha/2)"]
[16.2]
[16.899999999999999,null,"Step 5: Write Conclusion"]
[16.55,null,"Because the p-value of 0.15 > alpha of 0.05, we Fail To Reject H0"]
[16.25,null,"Because the test statistic of 1.44 is between -1.96 and 1.96, we Fail To Reject H0"]
[15.99,null,"The sample evidence suggests that the machine is filling properly."]
[16.350000000000001]
[16.079999999999998,null,"At an alpha of 0.05 the sample mean of 16.12 oz. does not provide statistically significant"]
[16.059999999999999,null,"evidence to suggest that the process is out of control."]
[16.36,null,"We do run a 5% risk of a Type 2 Error: We might say the machine is filling accurately, when it is not."]
[16.079999999999998]
[16.72]
[16.64]

{"sheet":"HT-z-Two-Tail (an)","index":6,"n_rows":56,"n_cols":16,"rows_kept":56,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting (Original Statement) H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"A bottle of \"Yummy Red Catsup\" is labeled as having 16 oz. of catsup. The bottle filling factory wants to make sure the filling machine is filling accurately. They do not want to fill too little and make customers unhappy, and they do not want to fill too much and thus decrease profits. At the alpha level of 0.05 is the process out of control? (From the companies data they estimate the population standard deviation to be 0.5 oz.)"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,".","Point of view:","Manufacturer wants to make sure that machine is filling accurately, not too much, not too little."]
[null,".","Considering:","Population of all possible bottles that could come off filling line."]
[null,".","Goal:","Run Hypothesis test to provide statistical evidence to show whether the machine is filling"]
[null,{"$f":"IF(B18=\"\",\"\",\".\")","v":"."},null,"accurately, yes, or no.",null,null,"Two Tail"]
["oz. per Bottle",null,"Step 1: List H0 and Ha","H0 : μ "," =",{"$f":"D26","v":16}]
[15.25,null,null,"Ha : μ "," <>",{"$f":"D26","v":16}]
[15.03]
[16.07,null,"Step 2: Select Alpha","Alpha =",0.05,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[16.260000000000002]
[16.22,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[15.49,null,"Hypothesized Mean = μ0 =",16]
[15.41,null,"Sigma = s =",0.5]
[17.522227666665689,null,"Sample SD = s","NA"]
[15.5,null,"Test Statistic To Use:","z",null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":"Because Sigma Known"}]
[16,null,"sample size = n",{"$f":"COUNT(A21:A56)","v":36}]
[16,null,"Sample Mean = Xbar",{"$f":"ROUND(AVERAGE(A21:A56),2)","v":16.12},null," =AVERAGE(values)"]
[16.66,null,"Alpha = a =",{"$f":"E23","v":0.05}]
[15.74,null,"Type of Test","Two Tail"]
[14.97,null,"SE",{"$f":"D27/SQRT(D30)","v":8.3333333333333329E-2},null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":" =Sigma/SQRT(n)"},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[15.6,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic = z ="},{"$f":"(D31-D26)/D34","v":1.4400000000000119},null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[16.13]
[15.96,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[17.21,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[16.64,null,"p-value Two Tail",{"$f":"_xlfn.NORM.S.DIST(-D35,1)*2","v":0.14986739906865065},null," =NORM.S.DIST(lower z,1)*2",null,null,"Probability of getting less than - Test Statistic or greatern than + Test Statistic"]
[15.65,null,null,{"$f":"(1-_xlfn.NORM.S.DIST(D35,1))*2","v":0.14986739906865054},null," =(1-NORM.S.DIST(upper z,1))*2"]
[16.07,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[16.62,null,"Rejection Rule:"," =-Critical Value  < Test Statistic < +Critical Value, Fail to Reject H0 , otherwsie Reject H0 and accept Ha "]
[16.59,null,"Lower Critial Value",{"$f":"_xlfn.NORM.S.INV(D32/2)","v":-1.9599639845400538},null," =NORM.S.INV(alpha/2)",null,null,"This is the hurdle Point"]
[15.7,null,"Upper Critial Value",{"$f":"-D43","v":1.9599639845400538},null," =-NORM.S.INV(alpha/2)"]
[16.2]
[16.899999999999999,null,"Step 5: Write Conclusion"]
[16.55,".","Because the p-value of 0.15 > alpha of 0.05, we Fail To Reject H0"]
[16.25,{"$f":"IF($B$47=\"\",\"\",\".\")","v":"."},"Because the test statistic of 1.44 is between -1.96 and 1.96, we Fail To Reject H0"]
[15.99,".","The sample evidence suggests that the machine is filling properly."]
[16.350000000000001,"."]
[16.079999999999998,".","At an alpha of 0.05 the sample mean of 16.12 oz. does not provide statistically significant"]
[16.059999999999999,".","evidence to suggest that the process is out of control."]
[16.36,".","We do run a 5% risk of a Type 2 Error: We might say the machine is filling accurately, when it is not."]
[16.079999999999998,"."]
[16.72]
[16.64]

{"sheet":"SummaryNORMFunctions","index":7,"n_rows":58,"n_cols":6,"rows_kept":58,"cut":false,"hidden":false,"merged":[]}
["1-Tail To Right - Upper"]
["Hypothesized Mean = μ0 =",85000]
["Sigma = s =",12549]
["sample size = n",36]
["Sample Mean = Xbar",88594.999999999971]
["Alpha = a =",0.05]
["SE",null," =Sigma/SQRT(n)","Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic = z =",null," =(Xbar - μ0)/SE","Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value One Tail To Right",null," =1-NORM.S.DIST(z,1)","Probability of getting Test Statistic or higher"]
["Rejection Rule: Test Statistic >= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Critical Value One Tail To Right",null," =NORM.S.INV(1-alpha)","This is the hurdle Point"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["1-Tail To Left - Lower"]
["Hypothesized Mean = μ0 =",16,"oz."]
["Sigma = s =",0.5,"oz."]
["sample size = n",100]
["Sample Mean = Xbar",15.96]
["Alpha = a =",0.05]
["SE",null," =Sigma/SQRT(n)","Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic =  =",null," =(Xbar - μ0)/SE","Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value One Tail To Left",null," =NORM.S.DIST(z,1)","Probability of getting Test Statistic or higher"]
["Rejection Rule: Test Statistic <= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Critical Value One Tail To Left",null," =NORM.S.INV(alpha)","This is the hurdle Point"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"p-value Two Tail"]
[]
[]
["Two Tail"]
["Hypothesized Mean = μ0 =",16]
["Sigma = s =",0.5]
["sample size = n",36]
["Sample Mean = Xbar",16.12]
["Alpha = a =",0.05]
["SE",null," =Sigma/SQRT(n)",null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic = z =",null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value Two Tail",null," =NORM.S.DIST(lower z,1)*2",null,null,"Probability of getting less than - Test Statistic or greatern than + Test Statistic"]
["Rejection Rule: =-Critical Value  < Test Statistic < +Critical Value, Fail to Reject H0 , otherwsie Reject H0 and accept Ha "]
["Lower Critial Value",null," =NORM.S.INV(alpha/2)",null,null,"This is the hurdle Point"]
["Upper Critial Value",null," =-NORM.S.INV(alpha/2)"]

{"sheet":"SummaryNORMFunctions (an)","index":8,"n_rows":58,"n_cols":6,"rows_kept":58,"cut":false,"hidden":false,"merged":[]}
["1-Tail To Right - Upper"]
["Hypothesized Mean = μ0 =",85000]
["Sigma = s =",12549]
["sample size = n",36]
["Sample Mean = Xbar",88594.999999999971]
["Alpha = a =",0.05]
["SE",{"$f":"B3/SQRT(B4)","v":2091.5}," =Sigma/SQRT(n)","Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic = z =",{"$f":"(B5-B2)/B7","v":1.718862060721956}," =(Xbar - μ0)/SE","Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value One Tail To Right",{"$f":"1-_xlfn.NORM.S.DIST(B8,1)","v":4.2819745911792384E-2}," =1-NORM.S.DIST(z,1)","Probability of getting Test Statistic or higher"]
["Rejection Rule: Test Statistic >= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Critical Value One Tail To Right",{"$f":"_xlfn.NORM.S.INV(1-B6)","v":1.6448536269514715}," =NORM.S.INV(1-alpha)","This is the hurdle Point"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["1-Tail To Left - Lower"]
["Hypothesized Mean = μ0 =",16,"oz."]
["Sigma = s =",0.5,"oz."]
["sample size = n",100]
["Sample Mean = Xbar",15.96]
["Alpha = a =",0.05]
["SE",{"$f":"B25/SQRT(B26)","v":0.05}," =Sigma/SQRT(n)","Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic =  =",{"$f":"(B27-B24)/B29","v":-0.79999999999998295}," =(Xbar - μ0)/SE","Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value One Tail To Left",{"$f":"_xlfn.NORM.S.DIST(B30,1)","v":0.21185539858340163}," =NORM.S.DIST(z,1)","Probability of getting Test Statistic or higher"]
["Rejection Rule: Test Statistic <= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Critical Value One Tail To Left",{"$f":"_xlfn.NORM.S.INV(B28)","v":-1.6448536269514726}," =NORM.S.INV(alpha)","This is the hurdle Point"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"p-value Two Tail",{"$f":"_xlfn.NORM.S.DIST(-B53,1)*2","v":0.14986739906865065}]
[]
[]
["Two Tail"]
["Hypothesized Mean = μ0 =",16]
["Sigma = s =",0.5]
["sample size = n",36]
["Sample Mean = Xbar",16.12]
["Alpha = a =",0.05]
["SE",{"$f":"B48/SQRT(B49)","v":8.3333333333333329E-2}," =Sigma/SQRT(n)",null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic = z =",{"$f":"(B50-B47)/B52","v":1.4400000000000119}," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value Two Tail",{"$f":"(1-_xlfn.NORM.S.DIST(B53,1))*2","v":0.14986739906865054}," =NORM.S.DIST(lower z,1)*2",null,null,"Probability of getting less than - Test Statistic or greatern than + Test Statistic"]
["Rejection Rule: =-Critical Value  < Test Statistic < +Critical Value, Fail to Reject H0 , otherwsie Reject H0 and accept Ha "]
["Lower Critial Value",{"$f":"_xlfn.NORM.S.INV(B51/2)","v":-1.9599639845400538}," =NORM.S.INV(alpha/2)",null,null,"This is the hurdle Point"]
["Upper Critial Value",{"$f":"-B57","v":1.9599639845400538}," =-NORM.S.INV(alpha/2)"]

{"sheet":"T & Histograms","index":9,"n_rows":24,"n_cols":4,"rows_kept":24,"cut":false,"hidden":false,"merged":[]}
["Q: When  are we allowed to use t Distribution?"]
["A: When population distribution in normally distributed or near normal, or n is sufficicently large enough"]
["1) If pop distribution is normal or near normal, smaller than 30 sample size may be used"]
["2) If pop distribution is not normal, n >= 30 usually adequate"]
["3) If pop distribution is highly skewed or has outliers, n >= 50 should be used"]
[]
["Notes:"]
["If the population distribution is not known a histogram based on a sample may give you a clue."]
["Although histogram is not conclusive, sometimes it may be the best clue that you have."]
["If the histogram shows non-normal or outliers, increasing the sample size and improve the calculations."]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[null,null,null,"At alpha = 0.05, 5% risk of rejecting H0 even though it was true, if we reject Mew <= $85,000, about 5 out of 100 times we will be incorrect."]

{"sheet":"HT-t-upper","index":10,"n_rows":81,"n_cols":16,"rows_kept":81,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"Fuses R Us manufactures fuses. A new machine for manufacturing fuses was installed. The old machine produced 250 fuse per hour. The manufacturer wants to determine if the new machine makes more than 250 fuses per hour. Over the last month a random sample of number of fuses made per hour was taken. At the 0.01 level of significance, can we conclude that the new machine produces more than 250 fuses per hour? Because this is a new machine, there is no data on what the population standard deviation is. The population distributions for manufacturing situations like this tends to be normally distributed (t-distribution requires that pop distribution is normal or near normal or n is large)."]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,null,"Point of view:","Manufacturer wants to see if new machines more productive"]
[null,null,"Considering:","Population of number of fuses made per hour from this machine"]
[null,null,"Goal:","Run Hypothesis test to provide statistical evidence to determine whether new"]
[null,null,null,"machine makes more than 250 fuse per hour.",null,null,null," >"]
[null,null,"Step 1: List H0 and Ha","H0 : μ",null,null,"# fuses per hour"]
["# fuses made",null,null,"Ha : μ",null,null,"# fuses per hour"]
[255]
[254,null,"Step 2: Select Alpha","Alpha =",null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[251]
[260,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[255,null,"Hypothesized Mean = μ0 ="]
[263,null,"Sigma = s ="]
[258,null,"Sample SD = s"]
[250,null,"Test Statistic To Use:",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":""}]
[260,null,"sample size = n",null,"df"]
[261,null,"Sample Mean = Xbar"]
[255,null,"Alpha = a ="]
[250,null,"Type of Test"]
[249,null,"SE",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":""},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[261,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic =  ="},null,null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[246]
[null,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[null,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[null,null,"p-value One Tail To Right",null,null," =1-T.DIST(t,df,1)",null,null,"Probability of getting Test Statistic or higher"]
[]
[null,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[null,null,"Rejection Rule:","Test Statistic >= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[null,null,"Critical Value One Tail To Right",null,null," =T.INV(1-alpha,df)",null,null,"This is the hurdle Point"]
[]
[]
[null,null,"Step 5: Write Conclusion"]
[null,null,"Because the p-value of 0.001 <= alpha of 0.01, we reject H0 and accept Ha. This is very strong evidence."]
[null,null,"Because the test statistic of 3.87 >= critical value of 2.62, we reject H0 and accept Ha."]
[null,null,"The statistical evidence very strongly suggests that the new machine is more productive than the old machine."]
[]
[null,null,"At an alpha of 0.01, our sample mean of 255 fuses made per hour provides statistically significant evidence"]
[null,null,"that the number of fuses made per hour is more than 250."]
[null,null,"We do run a 1% risk of a Type 1 Error that we might say that the mean number of fuses is more than 250,"]
[null,null,"when in fact it does not, however, the p-value provides very strong evidence that the machine is more"]
[null,null,"productive."]
[]
[]
[]
[]
["Min",{"$f":"MIN(A22:A36)","v":246}]
["Max",{"$f":"MAX(A22:A36)","v":263}]
[]
["Category","Frequency"]
[246,{"$f":"COUNTIF($A$22:$A$36,A64)","v":1}]
[247,{"$f":"COUNTIF($A$22:$A$36,A65)","v":0}]
[248,0]
[249,1]
[250,2]
[251,1]
[252,0]
[253,0]
[254,1]
[255,3]
[256,0]
[257,0]
[258,1]
[259,0]
[260,2]
[261,2]
[262,0]
[263,1]

{"sheet":"HT-t-upper (an)","index":11,"n_rows":81,"n_cols":16,"rows_kept":81,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"Fuses R Us manufactures fuses. A new machine for manufacturing fuses was installed. The old machine produced 250 fuse per hour. The manufacturer wants to determine if the new machine makes more than 250 fuses per hour. Over the last month a random sample of number of fuses made per hour was taken. At the 0.01 level of significance, can we conclude that the new machine produces more than 250 fuses per hour? Because this is a new machine, there is no data on what the population standard deviation is. The population distributions for manufacturing situations like this tends to be normally distributed (t-distribution requires that pop distribution is normal or near normal or n is large)."]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,".","Point of view:","Manufacturer wants to see if new machines more productive"]
[null,".","Considering:","Population of number of fuses made per hour from this machine"]
[null,".","Goal:","Run Hypothesis test to provide statistical evidence to determine whether new"]
[null,{"$f":"IF(B18=\".\",B18,\"\")","v":"."},null,"machine makes more than 250 fuse per hour.",null,null,null," >"]
[null,null,"Step 1: List H0 and Ha","H0 : μ"," <=",{"$f":"D26","v":250},"# fuses per hour"]
["# fuses made",null,null,"Ha : μ"," >",{"$f":"D26","v":250},"# fuses per hour"]
[255]
[254,null,"Step 2: Select Alpha","Alpha =",0.01,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[251]
[260,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[255,null,"Hypothesized Mean = μ0 =",250]
[263,null,"Sigma = s =","NA"]
[258,null,"Sample SD = s",{"$f":"_xlfn.STDEV.S(A22:A36)","v":5.1989009827627441}]
[250,null,"Test Statistic To Use:","t",null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":"Because Sigma NOT Known"}]
[260,null,"sample size = n",{"$f":"COUNT(A22:A36)","v":15},"df",{"$f":"D30-1","v":14}]
[261,null,"Sample Mean = Xbar",{"$f":"AVERAGE(A22:A36)","v":255.2}]
[255,null,"Alpha = a =",{"$f":"E23","v":0.01}]
[250,null,"Type of Test","One Tail To Right"]
[249,null,"SE",{"$f":"D28/SQRT(D30)","v":1.3423504616547655},null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":" =s/SQRT(n)"},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[261,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic = t ="},{"$f":"(D31-D26)/D34","v":3.8738020722172322},null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[246]
[null,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[null,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[null,null,"p-value One Tail To Right",{"$f":"1-_xlfn.T.DIST(D35,F30,1)","v":8.4327531292882618E-4},null," =1-T.DIST(t,df,1)",null,null,"Probability of getting Test Statistic or higher"]
[]
[null,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[null,null,"Rejection Rule:","Test Statistic >= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[null,null,"Critical Value One Tail To Right",{"$f":"_xlfn.T.INV(1-D32,F30)","v":2.6244940675900517},null," =T.INV(1-alpha,df)",null,null,"This is the hurdle Point"]
[]
[]
[null,null,"Step 5: Write Conclusion"]
[null,".","Because the p-value of 0.001 <= alpha of 0.01, we reject H0 and accept Ha. This is very strong evidence."]
[null,".","Because the test statistic of 3.87 >= critical value of 2.62, we reject H0 and accept Ha."]
[null,".","The statistical evidence very strongly suggests that the new machine is more productive than the old machine."]
[null,{"$f":"IF(B49=\".\",B49,\"\")","v":"."}]
[null,".","At an alpha of 0.01, our sample mean of 255 fuses made per hour provides statistically significant evidence"]
[null,{"$f":"IF(B51=\".\",B51,\"\")","v":"."},"that the number of fuses made per hour is more than 250."]
[null,".","We do run a 1% risk of a Type 1 Error that we might say that the mean number of fuses is more than 250,"]
[null,{"$f":"IF(B53=\".\",B53,\"\")","v":"."},"when in fact it does not, however, the p-value provides very strong evidence that the machine is more"]
[null,".","productive."]
[]
[]
[]
[]
["Min",{"$f":"MIN(A22:A36)","v":246}]
["Max",{"$f":"MAX(A22:A36)","v":263}]
[]
["Category","Frequency"]
[246,{"$f":"COUNTIF($A$22:$A$36,A64)","v":1}]
[247,{"$f":"COUNTIF($A$22:$A$36,A65)","v":0}]
[248,0]
[249,1]
[250,2]
[251,1]
[252,0]
[253,0]
[254,1]
[255,3]
[256,0]
[257,0]
[258,1]
[259,0]
[260,2]
[261,2]
[262,0]
[263,1]

{"sheet":"HT-t-lower","index":12,"n_rows":85,"n_cols":16,"rows_kept":85,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"Solid Construction is a company that builds decks for homes. The company recently employed a new building technique that is supposed to save time over the old method which had a mean of 15.5 hours. Solid Construction wants to determine if the new method actually saves time. A random sample was taken of number of hours to build a deck. At the .05 significance level, can Solid Construction conclude that the new method is faster?"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,null,"Point of view:","Solid Construction wants to see if the new method is faster"]
[null,null,"Considering:","Population of times for building a deck"]
[null,null,"Goal:","Run Hypothesis test to provide statistical evidence to determine whether new"]
[null,null,null,"method is faster than 15.5 hours",null,null,null," <"]
[null,null,"Step 1: List H0 and Ha","H0 : μ"]
["hours to build deck",null,null,"Ha : μ"]
[19.7]
[10.199999999999999,null,"Step 2: Select Alpha","Alpha =",null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[15.7]
[20,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[21.7,null,"Hypothesized Mean = μ0 ="]
[16,null,"Sigma = s ="]
[13.8,null,"Sample SD = s"]
[17.100000000000001,null,"Test Statistic To Use:",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":""}]
[19.399999999999999,null,"sample size = n",null,"df"]
[19.5,null,"Sample Mean = Xbar"]
[22.4,null,"Alpha = a ="]
[8.5,null,"Type of Test"]
[17.100000000000001,null,"SE",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":""},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[10.9,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic =  ="},null,null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[9.8000000000000007]
[12.7,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[15.5,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[11.8,null,"p-value One Tail To Left",null,null," =T.DIST(t,df,1)",null,null,"Probability of getting Test Statistic or lower"]
[9.5]
[10.5,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[18,null,"Rejection Rule:","Test Statistic <= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[14.3,null,"Critical Value One Tail To Left",null,null," =T.INV(alpha,df)",null,null,"This is the hurdle Point"]
[16.5]
[14.1]
[25.6,null,"Step 5: Write Conclusion"]
[17.8,null,"Because our p-value is bigger than out alpha, we Fail to Reject H0."]
[12.6,null,"Because our test statistic is bigger than our critical value, we Fail to Reject H0."]
[13.6,null,"The sample evidence does not suggest that the new method for building decks is faster. Because we did"]
[17.899999999999999,null,"get a sample mean of 14.9 hours and that is less than our hypothesized mean of 15.5 hours, we may want"]
[21,null,"to investigate further. Try a larger sample? Investigate whether or not the techniques of the new method"]
[19.5,null,"are being implemented properly?"]
[6.1,null,"At a 0.05 significance level, our sample mean of 14.9 hours does not provide statistical evidences to"]
[17.100000000000001,null,"support the idea that the new method reduces the time to build a new deck."]
[12.2,null,"We do run the risk of a Type 2 Error: Not accepting the alternative hypothesis (method faster), when in fact it was"]
[7.2]
[9.6]
[11.9]
[9.6999999999999993]
[20.2,null,"Min",{"$f":"MIN(A22:A71)","v":6.1}]
[17.8,null,"Max",{"$f":"MAX(A22:A71)","v":25.6}]
[18.100000000000001]
[13.4,null,"Category","Frequency"]
[21.8,null,6,{"$f":"COUNTIFS($A$22:$A$71,\">=\"&C64,$A$22:$A$71,\"<\"&C64+1)","v":1}]
[13,null,7,{"$f":"COUNTIFS($A$22:$A$71,\">=\"&C65,$A$22:$A$71,\"<\"&C65+1)","v":2}]
[7.7,null,8,1]
[15.8,null,9,4]
[14.9,null,10,4]
[13.9,null,11,3]
[11.7,null,12,3]
[10.3,null,13,5]
[null,null,14,3]
[null,null,15,3]
[null,null,16,2]
[null,null,17,6]
[null,null,18,2]
[null,null,19,4]
[null,null,20,2]
[null,null,21,3]
[null,null,22,1]
[null,null,23,0]
[null,null,24,0]
[null,null,25,1]
[null,null,26,0]
[null,null,"Total",{"$f":"SUM(D64:D84)","v":50}]

{"sheet":"HT-t-lower (an)","index":13,"n_rows":85,"n_cols":16,"rows_kept":85,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"Solid Construction is a company that builds decks for homes. The company recently employed a new building technique that is supposed to save time over the old method which had a mean of 15.5 hours. Solid Construction wants to determine if the new method actually saves time. A random sample was taken of number of hours to build a deck. At the .05 significance level, can Solid Construction conclude that the new method is faster?"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,".","Point of view:","Solid Construction wants to see if the new method is faster"]
[null,".","Considering:","Population of times for building a deck"]
[null,".","Goal:","Run Hypothesis test to provide statistical evidence to determine whether new"]
[null,{"$f":"IF(B18=\".\",B18,\"\")","v":"."},null,"method is faster than 15.5 hours",null,null,null," <"]
[null,null,"Step 1: List H0 and Ha","H0 : μ"," >=",{"$f":"$D$26","v":15.5},"hours to build a deck"]
["hours to build deck",null,null,"Ha : μ"," <",15.5,"hours to build a deck"]
[19.7]
[10.199999999999999,null,"Step 2: Select Alpha","Alpha =",0.05,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[15.7]
[20,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[21.7,null,"Hypothesized Mean = μ0 =",15.5]
[16,null,"Sigma = s =","NA"]
[13.8,null,"Sample SD = s",{"$f":"_xlfn.STDEV.S(A22:A71)","v":4.4784057841319891}]
[17.100000000000001,null,"Test Statistic To Use:","t",null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":"Because Sigma NOT Known"}]
[19.399999999999999,null,"sample size = n",{"$f":"COUNT(A22:A71)","v":50},"df",{"$f":"D30-1","v":49}]
[19.5,null,"Sample Mean = Xbar",{"$f":"AVERAGE(A22:A71)","v":14.902000000000003}]
[22.4,null,"Alpha = a =",{"$f":"E23","v":0.05}]
[8.5,null,"Type of Test","One Tail To Left"]
[17.100000000000001,null,"SE",{"$f":"D28/SQRT(D30)","v":0.63334221977295746},null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":" =s/SQRT(n)"},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[10.9,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic = t ="},{"$f":"(D31-D26)/D34","v":-0.94419727807561948},null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[9.8000000000000007]
[12.7,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[15.5,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[11.8,null,"p-value One Tail To Left",{"$f":"_xlfn.T.DIST(D35,F30,1)","v":0.17485072222630038},null," =T.DIST(t,df,1)",null,null,"Probability of getting Test Statistic or lower"]
[9.5]
[10.5,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[18,null,"Rejection Rule:","Test Statistic <= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[14.3,null,"Critical Value One Tail To Left",{"$f":"_xlfn.T.INV(D32,F30)","v":-1.6765508926168529},null," =T.INV(alpha,df)",null,null,"This is the hurdle Point"]
[16.5]
[14.1]
[25.6,null,"Step 5: Write Conclusion"]
[17.8,".","Because our p-value is bigger than out alpha, we Fail to Reject H0."]
[12.6,".","Because our test statistic is bigger than our critical value, we Fail to Reject H0."]
[13.6,".","The sample evidence does not suggest that the new method for building decks is faster. Because we did"]
[17.899999999999999,{"$f":"IF(B49=\".\",B49,\"\")","v":"."},"get a sample mean of 14.9 hours and that is less than our hypothesized mean of 15.5 hours, we may want"]
[21,{"$f":"IF(B50=\".\",B50,\"\")","v":"."},"to investigate further. Try a larger sample? Investigate whether or not the techniques of the new method"]
[19.5,{"$f":"IF(B51=\".\",B51,\"\")","v":"."},"are being implemented properly?"]
[6.1,".","At a 0.05 significance level, our sample mean of 14.9 hours does not provide statistical evidences to"]
[17.100000000000001,{"$f":"IF(B53=\".\",B53,\"\")","v":"."},"support the idea that the new method reduces the time to build a new deck."]
[12.2,".","We do run the risk of a Type 2 Error: Not accepting the alternative hypothesis (method faster), when in fact it was"]
[7.2]
[9.6]
[11.9]
[9.6999999999999993]
[20.2,null,"Min",{"$f":"MIN(A22:A71)","v":6.1}]
[17.8,null,"Max",{"$f":"MAX(A22:A71)","v":25.6}]
[18.100000000000001]
[13.4,null,"Category","Frequency"]
[21.8,null,6,{"$f":"COUNTIFS($A$22:$A$71,\">=\"&C64,$A$22:$A$71,\"<\"&C64+1)","v":1}]
[13,null,7,{"$f":"COUNTIFS($A$22:$A$71,\">=\"&C65,$A$22:$A$71,\"<\"&C65+1)","v":2}]
[7.7,null,8,1]
[15.8,null,9,4]
[14.9,null,10,4]
[13.9,null,11,3]
[11.7,null,12,3]
[10.3,null,13,5]
[null,null,14,3]
[null,null,15,3]
[null,null,16,2]
[null,null,17,6]
[null,null,18,2]
[null,null,19,4]
[null,null,20,2]
[null,null,21,3]
[null,null,22,1]
[null,null,23,0]
[null,null,24,0]
[null,null,25,1]
[null,null,26,0]
[null,null,"Total",{"$f":"SUM(D64:D84)","v":50}]

{"sheet":"HT-t-Two-Tail","index":14,"n_rows":96,"n_cols":16,"rows_kept":96,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"A report stated that the national mean price for a used cars is $9500. You want to dertermine if the Seattle area mean price of a used cars is differenet from the national mean. At an alpha of 0.01, is the mean price for a Seattle used cars different from the national average?"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,null,"Point of view:","Seattle Area Resercher who wants to compare national mean used car price to Seattle's"]
[null,null,"Considering:","Population of Seattle Used Car Prices"]
[null,null,"Goal:","Run Hypothesis test to provide statistical evidence to determine whether Seattle"]
[null,null,null,"used auto prices different from national mean"]
[null,null,"Step 1: List H0 and Ha","H0 : μ"]
["Car Price",null,null,"Ha : μ"]
[11696]
[13251,null,"Step 2: Select Alpha","Alpha =",null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[12482]
[11102,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[8062,null,"Hypothesized Mean = μ0 ="]
[10275,null,"Sigma = s ="]
[6065,null,"Sample SD = s"]
[5321,null,"Test Statistic To Use:",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":""}]
[10555,null,"sample size = n",null,"df"]
[10013,null,"Sample Mean = Xbar"]
[8049,null,"Alpha = a ="]
[9321,null,"Type of Test"]
[7024,null,"SE",null,null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":""},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[6448,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic =  ="},null,null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[10715]
[10854,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[9368,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[6017,null,"p-value Two Tail",null,null," =(1-T.DIST(t,df,1))*2",null,null,"Probability of getting Test Statistic or higher"]
[14177,null,null,null,null," =T.DIST.2T(ABS(t),df)",null,null,"ABS(t) because T.DIST.2T needs upper t"]
[10326,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[12576,null,"Rejection Rule:"," =-Critical Value  < Test Statistic < +Critical Value, Fail to Reject H0 , otherwsie Reject H0 and accept Ha "]
[6251,null,"Lower Critical Value",null,null," =T.INV(alpha/2,df)",null,null,null," =-T.INV.2T(alpha,df)",null,"This is the hurdle Point"]
[6995,null,"Upper Critical Value",null,null," =-T.INV(alpha/2,df)",null,null,null," =T.INV.2T(alpha,df)"]
[10682]
[10477,null,"Step 5: Write Conclusion"]
[10943,null,"Because our p-value is bigger than our alpha, we Fail to Reject H0."]
[8483,null,"Because our test statistic is between our critical values, we Fail to Reject H0."]
[13148,null,"The sample evidence does not suggest that the mean price for a used car in the Seattle area is different"]
[8954,null,"from the national average."]
[9210,null,"At a 0.01 significance level, our sample mean of $9923 does not provide statistical evidences to show that"]
[7960,null,"the mean Seattle used car price is different from the national mean."]
[9849,null,"We do run the risk of a Type 2 Error: Not accepting the alternative hypothesis (mean different from), when"]
[9001,null,"in fact it is different from"]
[12477]
[8494]
[3741]
[8846]
[8824]
[11815]
[13603]
[10410]
[8005]
[7886]
[9597]
[9856]
[12472]
[6851]
[9488]
[7359]
[11092]
[9383]
[11402]
[11531]
[12802]
[12078]
[6545]
[13161]
[8659]
[13203]
[13937]
[9603]
[7932]
[12777]
[7650]
[10793]
[15008]
[6439]
[11576]
[14726]
[10480]
[7696]
[11156]
[8900]
[10322]
[9966]

{"sheet":"HT-t-Two-Tail (an)","index":15,"n_rows":96,"n_cols":16,"rows_kept":96,"cut":false,"hidden":false,"merged":[]}
[null,null,"Mew = population mean = μ",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Left"]
[null,null,"Sigma = population standard deviation = s",null,null,null,null,null,null,null,null,null,null,null,null,"One Tail To Right"]
[null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE",null,null,null,null,null,null,null,null,null,null,null,null,"Two Tail"]
[null,null,"Hypothesized Value of Population Mean = μ0 = Assumed Value of Population Mean used for testing procedure"]
[null,null,"sample size = n"]
[null,null,"Sample Mean = Xbar"]
[null,null,"Sample Standard Deviation (for when sigma not known) = s"]
[null,null,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[null,null,"Test Statistic = Used to determine whether to reject H0 and accept Ha = Number of SE above or below hypothesized mean"]
[null,null,"Use z test statistic if Sigma known or can be estimated, or you are significance Testing a Proportion and all 4 binomial tests have been met"]
[null,null,"Use t test statistic if Sigma NOT known or can be estimated"]
[]
[null,null,"A report stated that the national mean price for a used cars is $9500. You want to dertermine if the Seattle area mean price of a used cars is differenet from the national mean. At an alpha of 0.01, is the mean price for a Seattle used cars different from the national average?"]
[]
[null,null,"Hypothesis Test (Significance Test)"]
[null,".","Point of view:","Seattle Area Resercher who wants to compare national mean used car price to Seattle's"]
[null,".","Considering:","Population of Seattle Used Car Prices"]
[null,".","Goal:","Run Hypothesis test to provide statistical evidence to determine whether Seattle"]
[null,{"$f":"IF(B18=\".\",B18,\"\")","v":"."},null,"used auto prices different from national mean"]
[null,null,"Step 1: List H0 and Ha","H0 : μ"," =",{"$f":"D26","v":9500},"Mean Used Car price"]
["Car Price",null,null,"Ha : μ"," <>",{"$f":"D26","v":9500},"Mean Used Car price"]
[11696]
[13251,null,"Step 2: Select Alpha","Alpha =",0.01,"Alpha = a = Risk of rejecting H0 when it is actually true = Type 1 Error"]
[12482]
[11102,null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
[8062,null,"Hypothesized Mean = μ0 =",9500]
[10275,null,"Sigma = s =","NA"]
[6065,null,"Sample SD = s",{"$f":"_xlfn.STDEV.S(A22:A96)","v":2405.9022092263776}]
[5321,null,"Test Statistic To Use:","t",null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\"Because Sigma Known\",IF(D29=\"t\",\"Because Sigma NOT Known\",\"Please Enter a z or t\")))","v":"Because Sigma NOT Known"}]
[10555,null,"sample size = n",{"$f":"COUNT(A22:A96)","v":75},"df",{"$f":"D30-1","v":74}]
[10013,null,"Sample Mean = Xbar",{"$f":"AVERAGE(A22:A96)","v":9922.5466666666671}]
[8049,null,"Alpha = a =",{"$f":"E23","v":0.01}]
[9321,null,"Type of Test","Two Tail"]
[7024,null,"SE",{"$f":"D28/SQRT(D30)","v":277.80965762815288},null,{"$f":"IF(D29=\"\",\"\",IF(D29=\"z\",\" =Sigma/SQRT(n)\",IF(D29=\"t\",\" =s/SQRT(n)\",IF(OR(D29<>\"z\",D29<>\"t\"),\".\"))))","v":" =s/SQRT(n)"},null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
[6448,null,{"$f":"\"Test Statistic = \"&IF(D29=\"z\",\"z\",IF(D29=\"t\",\"t\",\"\"))&\" =\"","v":"Test Statistic = t ="},{"$f":"(D31-D26)/D34","v":1.5209934394442259},null," =(Xbar - μ0)/SE",null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
[10715]
[10854,null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
[9368,null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
[6017,null,"p-value Two Tail",{"$f":"(1-_xlfn.T.DIST(D35,F30,1))*2","v":0.13252318759690596},null," =(1-T.DIST(t,df,1))*2",null,null,"Probability of getting Test Statistic or higher"]
[14177,null,null,{"$f":"_xlfn.T.DIST.2T(ABS(D35),F30)","v":0.13252318759690598},null," =T.DIST.2T(ABS(t),df)",null,null,"ABS(t) because T.DIST.2T needs upper t"]
[10326,null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
[12576,null,"Rejection Rule:"," =-Critical Value  < Test Statistic < +Critical Value, Fail to Reject H0 , otherwsie Reject H0 and accept Ha "]
[6251,null,"Lower Critical Value",{"$f":"_xlfn.T.INV(D32/2,F30)","v":-2.64391287165309},null," =T.INV(alpha/2,df)",null,null,{"$f":"-I44","v":-2.64391287165309}," =-T.INV.2T(alpha,df)",null,"This is the hurdle Point"]
[6995,null,"Upper Critical Value",{"$f":"-D43","v":2.64391287165309},null," =-T.INV(alpha/2,df)",null,null,{"$f":"_xlfn.T.INV.2T(D32,F30)","v":2.64391287165309}," =T.INV.2T(alpha,df)"]
[10682]
[10477,null,"Step 5: Write Conclusion"]
[10943,".","Because our p-value is bigger than our alpha, we Fail to Reject H0."]
[8483,".","Because our test statistic is between our critical values, we Fail to Reject H0."]
[13148,".","The sample evidence does not suggest that the mean price for a used car in the Seattle area is different"]
[8954,{"$f":"IF(B49=\".\",B49,\"\")","v":"."},"from the national average."]
[9210,".","At a 0.01 significance level, our sample mean of $9923 does not provide statistical evidences to show that"]
[7960,{"$f":"IF(B51=\".\",B51,\"\")","v":"."},"the mean Seattle used car price is different from the national mean."]
[9849,".","We do run the risk of a Type 2 Error: Not accepting the alternative hypothesis (mean different from), when"]
[9001,{"$f":"IF(B53=\".\",B53,\"\")","v":"."},"in fact it is different from"]
[12477]
[8494]
[3741]
[8846]
[8824]
[11815]
[13603]
[10410]
[8005]
[7886]
[9597]
[9856]
[12472]
[6851]
[9488]
[7359]
[11092]
[9383]
[11402]
[11531]
[12802]
[12078]
[6545]
[13161]
[8659]
[13203]
[13937]
[9603]
[7932]
[12777]
[7650]
[10793]
[15008]
[6439]
[11576]
[14726]
[10480]
[7696]
[11156]
[8900]
[10322]
[9966]

{"sheet":"SummaryTFunctions","index":16,"n_rows":48,"n_cols":7,"rows_kept":48,"cut":false,"hidden":false,"merged":[]}
["1-Tail To Right - Upper"]
["Hypothesized Mean = μ0 =",250]
["Sample SD = s",5.1989009827627441]
["sample size = n",15]
["df",null," =n-NumberOfSamples"]
["Sample Mean = Xbar",255.2]
["Alpha = a =",0.01]
["SE",null," =s/SQRT(n)",null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic = t =",null," =(Xbar - μ0)/SE",null,null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value One Tail To Right",null," =1-T.DIST(t,df,1)",null,null,null,"Probability of getting Test Statistic or higher"]
["p-value One Tail To Right",null," =T.DIST.RT(t,df)"]
["Rejection Rule: Test Statistic >= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Critical Value One Tail To Right",null," =T.INV(1-alpha,df)",null,null,null,"This is the hurdle Point"]
[]
["1-Tail To Left - Lower"]
["Hypothesized Mean = μ0 =",15.5]
["Sample SD = s",4.4784057841319891]
["sample size = n",50]
["df",{"$f":"B19-1","v":49}," =n-NumberOfSamples"]
["Sample Mean = Xbar",14.902000000000003]
["Alpha = a =",0.05]
["SE",{"$f":"B18/SQRT(B19)","v":0.63334221977295746}," =s/SQRT(n)",null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic = t =",{"$f":"(B21-B17)/B23","v":-0.94419727807561948}," =(Xbar - μ0)/SE",null,null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value One Tail To Left",null," =T.DIST(t,df,1)",null,null,null,"Probability of getting Test Statistic or lower"]
["Rejection Rule: Test Statistic <= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Critical Value One Tail To Left",null," =T.INV(alpha,df)",null,null,null,"This is the hurdle Point"]
[]
[]
["Two Tail"]
["Hypothesized Mean = μ0 =",9500]
["Sample SD = s",2405.9022092263776]
["sample size = n",75,"df",74]
["df",{"$f":"B34-1","v":74}," =n-NumberOfSamples"]
["Sample Mean = Xbar",9922.5466666666671]
["Alpha = a =",0.01]
["SE",{"$f":"B33/SQRT(B34)","v":277.80965762815288}," =s/SQRT(n)",null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic = t =",{"$f":"(B36-B32)/B38","v":1.5209934394442259}," =(Xbar - μ0)/SE",null,null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value Two Tail",null," =(1-T.DIST(t,df,1))*2",null,null,null,"Probability of getting Test Statistic or higher"]
["p-value Two Tail",null," =T.DIST.2T(ABS(t),df)",null,null,null,"ABS(t) because T.DIST.2T needs upper t"]
["Rejection Rule: Test Statistic <= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Lower Critical Value",null," =T.INV(alpha/2,df)"]
["Upper Critical Value",null," =-T.INV(alpha/2,df)"]
[]
["Lower Critical Value",null," =-T.INV.2T(alpha,df)"]
["Upper Critical Value",null," =T.INV.2T(alpha,df)"]

{"sheet":"SummaryTFunctions (an)","index":17,"n_rows":48,"n_cols":7,"rows_kept":48,"cut":false,"hidden":false,"merged":[]}
["1-Tail To Right - Upper"]
["Hypothesized Mean = μ0 =",250]
["Sample SD = s",5.1989009827627441]
["sample size = n",15]
["df",{"$f":"B4-1","v":14}," =n-NumberOfSamples"]
["Sample Mean = Xbar",255.2]
["Alpha = a =",0.01]
["SE",{"$f":"B3/SQRT(B4)","v":1.3423504616547655}," =s/SQRT(n)",null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic = t =",{"$f":"(B6-B2)/B8","v":3.8738020722172322}," =(Xbar - μ0)/SE",null,null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value One Tail To Right",{"$f":"1-_xlfn.T.DIST(B9,B5,1)","v":8.4327531292882618E-4}," =1-T.DIST(t,df,1)",null,null,null,"Probability of getting Test Statistic or higher"]
["p-value One Tail To Right",{"$f":"_xlfn.T.DIST.RT(B9,B5)","v":8.4327531292878693E-4}," =T.DIST.RT(t,df)"]
["Rejection Rule: Test Statistic >= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Critical Value One Tail To Right",{"$f":"_xlfn.T.INV(1-B7,B5)","v":2.6244940675900517}," =T.INV(1-alpha,df)",null,null,null,"This is the hurdle Point"]
[]
["1-Tail To Left - Lower"]
["Hypothesized Mean = μ0 =",15.5]
["Sample SD = s",4.4784057841319891]
["sample size = n",50]
["df",{"$f":"B19-1","v":49}," =n-NumberOfSamples"]
["Sample Mean = Xbar",14.902000000000003]
["Alpha = a =",0.05]
["SE",{"$f":"B18/SQRT(B19)","v":0.63334221977295746}," =s/SQRT(n)",null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic = t =",{"$f":"(B21-B17)/B23","v":-0.94419727807561948}," =(Xbar - μ0)/SE",null,null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value One Tail To Left",{"$f":"_xlfn.T.DIST(B24,B20,1)","v":0.17485072222630038}," =T.DIST(t,df,1)",null,null,null,"Probability of getting Test Statistic or lower"]
["Rejection Rule: Test Statistic <= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Critical Value One Tail To Left",{"$f":"_xlfn.T.INV(B22,B20)","v":-1.6765508926168529}," =T.INV(alpha,df)",null,null,null,"This is the hurdle Point"]
[]
[]
["Two Tail"]
["Hypothesized Mean = μ0 =",9500]
["Sample SD = s",2405.9022092263776]
["sample size = n",75,"df",74]
["df",{"$f":"B34-1","v":74}," =n-NumberOfSamples"]
["Sample Mean = Xbar",9922.5466666666671]
["Alpha = a =",0.01]
["SE",{"$f":"B33/SQRT(B34)","v":277.80965762815288}," =s/SQRT(n)",null,null,"Standard Error = Standard Deviation for the Sampling distribution of Xbar = SE"]
["Test Statistic = t =",{"$f":"(B36-B32)/B38","v":1.5209934394442259}," =(Xbar - μ0)/SE",null,null,"Sample Error in numerator, Standard Deviations in Denominator = \"How Many SD above or below Hypothesized Pop Mean"]
["Rejection Rule: p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["p-value Two Tail",{"$f":"(1-_xlfn.T.DIST(B39,B35,1))*2","v":0.13252318759690596}," =(1-T.DIST(t,df,1))*2",null,null,null,"Probability of getting Test Statistic or higher"]
["p-value Two Tail",{"$f":"_xlfn.T.DIST.2T(ABS(B39),B35)","v":0.13252318759690598}," =T.DIST.2T(ABS(t),df)",null,null,null,"ABS(t) because T.DIST.2T needs upper t"]
["Rejection Rule: Test Statistic <= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Lower Critical Value",{"$f":"_xlfn.T.INV(B37/2,B35)","v":-2.64391287165309}," =T.INV(alpha/2,df)"]
["Upper Critical Value",{"$f":"-B44","v":2.64391287165309}," =-T.INV(alpha/2,df)"]
[]
["Lower Critical Value",{"$f":"-B48","v":-2.64391287165309}," =-T.INV.2T(alpha,df)"]
["Upper Critical Value",{"$f":"_xlfn.T.INV.2T(B37,B35)","v":2.64391287165309}," =T.INV.2T(alpha,df)"]

{"sheet":"Proportion","index":18,"n_rows":155,"n_cols":7,"rows_kept":155,"cut":false,"hidden":false,"merged":[]}
["The School Newspaper stated that the proportion of students who knew when the presidential election would be held was 15%. A researcher thought that this was low and wanted to show that the proportion of students who knew when the presidential election would be held is higher than 15%. The researcher took a random sample and made sure that he got respondents from all of the different demographics, including night students, online students, new immigrants and others. At alpha = 0.01, can the researcher conclude that more than 15% of the students know when the presidential election will be held?"]
[]
["Knew When Election Was",null,"Binomial?"]
["No",null,"Fixed Number of Trials?","Yes"]
["No",null,"Prob stays same each time","Yes","Yes or No"]
["No",null,"Trials are independent","Yes","(randomly selected and not all grouped together by similar traits)"]
["Yes",null,"Each Trial result in success or not success","Yes","Yes or No"]
["No",null,"Assume True: n*p >= 5",{"$f":"D17*D12","v":22.8},{"$f":"IF(D8>=5,\"Yes\",\"No\")","v":"Yes"}]
["No",null,"Assume True: n*(1-p) >= 5",{"$f":"(1-D12)*D17","v":129.19999999999999},"Yes"]
["Yes",null,"Success =","Yes","Know when election is"]
["No",null,"Not Success","No","Does not know"]
["No",null,"Hypothesized Pop Proportion = p0 =",0.15]
["No",".","Point of view:","Researcher who was skeptical of reported proportion of the number students know when the presidential election is"]
["No",".","Goal:","Test to see if there is significantly more than 15% of the students who know when the"]
["Yes",{"$f":"IF(B14=\"\",\"\",\".\")","v":"."},null,"presidential election will be held."]
["No",null,"Test:"," >>>>>>> 1 tail to right"]
["No",null,"n = students",{"$f":"COUNTA(A4:A155)","v":152},null,"=COUNTA(A4:A155)","Relative Frequency from Chapter 2"]
["Yes",null,{"$f":"\"Count for \"&D10","v":"Count for Yes"},null,null,"=COUNTIF($A$4:$A$155,D10)","Relative Frequency from Chapter 2"]
["No",null,{"$f":"\"Count for \"&D11","v":"Count for No"},null,null,"=COUNTIF($A$4:$A$155,D11)"]
["Yes",null,{"$f":"\"Prob(\"&D10&\")\"","v":"Prob(Yes)"},null,null,"=D18/$D$17"]
["No",null,{"$f":"\"Prob(\"&D11&\")\"","v":"Prob(No)"},null,null,"=D19/$D$17"]
["No"]
["No",null,"Step 1:"]
["No",null,"H0 : p"]
["No",null,"Ha : p"]
["No"]
["No",null,"Step 2:","alpha"]
["Yes"]
["No",null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
["No",null,{"$f":"C20&\" = Pbar =\"","v":"Prob(Yes) = Pbar ="}]
["Yes",null,"SE",null,null," =SQRT(p0*(1-p0)/n)"]
["No",null,"Test Statistic = z",null,null," =(Pbar - p0)/SE"]
["Yes"]
["No",null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
["No",null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Yes",null,"p-value One Tail To Right",null,null," =1-NORM.S.DIST(z,1)"]
["No"]
["No",null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
["No",null,"Rejection Rule:","Test Statistic >= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Yes",null,"Critical Value One Tail To Right",null,null," =NORM.S.INV(1-E27)"]
["No"]
["No",null,"Step 5: Write Conclusion"]
["Yes",".","Because the p-value of 0.0014 is less than or equal to our alpha of 0.01, we Reject H0 and accept Ha"]
["No",".","Because the Test Statistics of 2.998 is greater than or equal to our Critical Value of 2.33, we Reject H0 and accept Ha"]
["Yes",".","There is strong statistical evidence to support the claim that more than 15% of the students know when the presidential election will be held."]
["No",".","At an alpha of 0.01, our sample proportion of 0.24 provides very strong statistical evidence to suggest that more than 15% of the"]
["No",{"$f":"IF(B46=\"\",\"\",\".\")","v":"."},"students know when the presidential election will be held."]
["No",".","We do run 1% Type 1 Error risk of saying that more than 15% of the students know when the election will be, when they in fact do not know."]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["Yes"]
["No"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]

{"sheet":"Proportion (an)","index":19,"n_rows":155,"n_cols":7,"rows_kept":155,"cut":false,"hidden":false,"merged":[]}
["The School Newspaper stated that the proportion of students who knew when the presidential election would be held was 15%. A researcher thought that this was low and wanted to show that the proportion of students who knew when the presidential election would be held is higher than 15%. The researcher took a random sample and made sure that he got respondents from all of the different demographics, including night students, online students, new immigrants and others. At alpha = 0.01, can the researcher conclude that more than 15% of the students know when the presidential election will be held?"]
[]
["Knew When Election Was",null,"Binomial?"]
["No",null,"Fixed Number of Trials?","Yes"]
["No",null,"Prob stays same each time","Yes","Yes or No"]
["No",null,"Trials are independent","Yes","(randomly selected and not all grouped together by similar traits)"]
["Yes",null,"Each Trial result in success or not success","Yes","Yes or No"]
["No",null,"Assume True: n*p >= 5",{"$f":"D17*D12","v":22.8},{"$f":"IF(D8>=5,\"Yes\",\"No\")","v":"Yes"}]
["No",null,"Assume True: n*(1-p) >= 5",{"$f":"(1-D12)*D17","v":129.19999999999999},"Yes"]
["Yes",null,"Success =","Yes","Know when election is"]
["No",null,"Not Success","No","Does not know"]
["No",null,"Hypothesized Pop Proportion = p0 =",0.15]
["No",".","Point of view:","Researcher who was skeptical of reported proportion of the number students know when the presidential election is"]
["No",".","Goal:","Test to see if there is significantly more than 15% of the students who know when the"]
["Yes",{"$f":"IF(B14=\"\",\"\",\".\")","v":"."},null,"presidential election will be held."]
["No",null,"Test:"," >>>>>>> 1 tail to right"]
["No",null,"n = students",{"$f":"COUNTA(A4:A155)","v":152},null,"=COUNTA(A4:A155)","Relative Frequency from Chapter 2"]
["Yes",null,{"$f":"\"Count for \"&D10","v":"Count for Yes"},{"$f":"COUNTIF($A$4:$A$155,D10)","v":36},null,"=COUNTIF($A$4:$A$155,D10)","Relative Frequency from Chapter 2"]
["No",null,{"$f":"\"Count for \"&D11","v":"Count for No"},{"$f":"COUNTIF($A$4:$A$155,D11)","v":116},null,"=COUNTIF($A$4:$A$155,D11)"]
["Yes",null,{"$f":"\"Prob(\"&D10&\")\"","v":"Prob(Yes)"},{"$f":"D18/$D$17","v":0.23684210526315788},null,"=D18/$D$17"]
["No",null,{"$f":"\"Prob(\"&D11&\")\"","v":"Prob(No)"},{"$f":"D19/$D$17","v":0.76315789473684215},null,"=D19/$D$17"]
["No"]
["No",null,"Step 1:"]
["No",null,"H0 : p"," <=",{"$f":"D12","v":0.15}]
["No",null,"Ha : p"," >",{"$f":"D12","v":0.15}]
["No"]
["No",null,"Step 2:","alpha",0.01]
["Yes"]
["No",null,"Step 3: Draw Picture, Collect Data, Calculate Sample Statistics, Calculate Test Statistic"]
["No",null,{"$f":"C20&\" = Pbar =\"","v":"Prob(Yes) = Pbar ="},{"$f":"D20","v":0.23684210526315788}]
["Yes",null,"SE",{"$f":"SQRT(D12*(1-D12)/D17)","v":2.8962316714546237E-2},null," =SQRT(p0*(1-p0)/n)"]
["No",null,"Test Statistic = z",{"$f":"(D30-D12)/D31","v":2.9984516128000802},null," =(Pbar - p0)/SE"]
["Yes"]
["No",null,"Step 4: Create p-value Rejection Rule and calculate p-value"]
["No",null,"Rejection Rule:","p-value <= alpha, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Yes",null,"p-value One Tail To Right",{"$f":"1-_xlfn.NORM.S.DIST(D32,1)","v":1.3567762089927715E-3},null," =1-NORM.S.DIST(z,1)"]
["No"]
["No",null,"Step 4: Calculate Critical Value and Critical Value Rejection Rule"]
["No",null,"Rejection Rule:","Test Statistic >= Critical Value, Reject H0 and accept Ha , otherwise Fail to Reject H0"]
["Yes",null,"Critical Value One Tail To Right",{"$f":"_xlfn.NORM.S.INV(1-E27)","v":2.3263478740408408},null," =NORM.S.INV(1-E27)"]
["No"]
["No",null,"Step 5: Write Conclusion"]
["Yes",".","Because the p-value of 0.0014 is less than or equal to our alpha of 0.01, we Reject H0 and accept Ha"]
["No",".","Because the Test Statistics of 2.998 is greater than or equal to our Critical Value of 2.33, we Reject H0 and accept Ha"]
["Yes",".","There is strong statistical evidence to support the claim that more than 15% of the students know when the presidential election will be held."]
["No",".","At an alpha of 0.01, our sample proportion of 0.24 provides very strong statistical evidence to suggest that more than 15% of the"]
["No",{"$f":"IF(B46=\"\",\"\",\".\")","v":"."},"students know when the presidential election will be held."]
["No",".","We do run 1% Type 1 Error risk of saying that more than 15% of the students know when the election will be, when they in fact do not know."]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["No"]
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["No"]
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["No"]
["Yes"]
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["No"]
["No"]
["Yes"]
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["No"]
["No"]
["No"]
["No"]
["Yes"]
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["No"]
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["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
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["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["Yes"]
["No"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]