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["Chapter 8: Confidence Intervals (Interval Estimation)"]
["Ch 7 (Pop. Mean, μ, Known) compared to Ch 8 (Pop. Mean, μ, NOT Known)"]
["Estimate Population Mean (μ): μ NOT Known and s Known -- Use z Distribution"]
["Estimate Population Mean (μ): μ NOT Known and NOT s Known -- Use t Distribution"]
["Estimate Population Proportion (p): Use z Distribution"]
["Estimate Sample Size"]

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[{"$f":"\"An insurance company claims that the average cost per year for a policy is \"&DOLLAR(B7,0)&\".\"","v":"An insurance company claims that the average cost per year for a policy is $822."},null,null,null,null,null,null,null,null,"Sample"]
[{"$f":"\"The standard deviation for the population is \"&DOLLAR(B8,0)&\".\"","v":"The standard deviation for the population is $202."},null,null,null,null,null,null,null,null,716]
[{"$f":"\"What is the probability of getting a sample mean within +/- \"&DOLLAR(B9)&\"?\"","v":"What is the probability of getting a sample mean within +/- $23.32?"},null,null,null,null,null,null,null,null,926]
["If you take a random sample and get a sample mean of ",null,null,null,null,null,null,null,null,722]
[{"$f":"DOLLAR(B13,0)&\" (n = \"&B10&\"), is the claim reasonable?\"","v":"$850 (n = 300), is the claim reasonable?"},null,null,null,null,null,null,null,null,810]
[null,null,null,null,null,null,null,null,null,873]
["Mew",822,"Annual Auto Insurance Cost",null,null,null,null,null,null,873]
["Sigma",202,null,null,null,null,null,null,null,1074]
["Margin of error = Standard Error * 2",{"$f":"B14*2","v":23.324950875260878},null,null,null,null,null,null,null,1135]
["n",{"$f":"COUNT(J2:J301)","v":300},null,null,null,null,null,null,null,763]
["N",25000,null,null,null,null,null,null,null,1074]
["n/N",{"$f":"B10/B11","v":1.2E-2},null,{"$f":"IF(B12=\"\",\"\",\"less than 0.05, don't need SQRT((N-n)/(N-1))\")","v":"less than 0.05, don't need SQRT((N-n)/(N-1))"},null,null,null,null,null,675]
["Sample Xbar - Point Estimate of Population Parameter",{"$f":"ROUND(AVERAGE(J2:J301),0)","v":850},null,null,null,null,null,null,null,824]
["Standard Error",{"$f":"B8/SQRT(B10)","v":11.662475437630439},null,null,null,null,null,null,null,988]
["Low Xbar",{"$f":"$B$7-$B$9","v":798.67504912473908},null,null,null,null,null,null,null,873]
["High Xbar",{"$f":"$B$7+$B$9","v":845.32495087526092},null,null,null,null,null,null,null,824]
[{"$f":"\"P(\"&DOLLAR(B15)&\" <= Xbar <= \"&DOLLAR(B16)&\")\"","v":"P($798.68 <= Xbar <= $845.32)"},{"$f":"_xlfn.NORM.DIST(B16,B7,B14,1)-_xlfn.NORM.DIST(B15,B7,B14,1)","v":0.95449973610364203},null,null,null,null,null,null,null,873]
["Conclusion:",null,null,null,null,null,null,null,null,622]
["Xbar is only a point estimate of μ. The difference is always Sampling Error (Xbar - μ).",null,null,null,null,null,null,null,null,1074]
["Is our sampling error acceptable, or NOT acceptable?",null,null,null,null,null,null,null,null,867]
["Statements we are allowed to make:",null,null,null,null,null,null,null,null,824]
["We know Mew, μ, and we make a statement about the probability that Xbar lies within an interval.",null,null,null,null,null,null,null,null,722]
[{"$f":"\"We are \"&TEXT($B$17,\"0%\")&\" sure that our Xbar will lie between \"&DOLLAR($B$15)&\" and \"&DOLLAR($B$16)&\".\"","v":"We are 95% sure that our Xbar will lie between $798.68 and $845.32."},null,null,null,null,null,null,null,null,703]
[{"$f":"\"We run a \"&TEXT(1-$B$17,\"0%\")&\" that our Xbar will lie OUTSIDE the interval \"&DOLLAR($B$15)&\" and \"&DOLLAR($B$16)&\".\"","v":"We run a 5% that our Xbar will lie OUTSIDE the interval $798.68 and $845.32."},null,null,null,null,null,null,null,null,824]
[{"$f":"\"The probability is \"&TEXT($B$17,\"0%\")&\" that our Xbar lies with in +/- \"&DOLLAR(B9)&\".\"","v":"The probability is 95% that our Xbar lies with in +/- $23.32."},null,null,null,null,null,null,null,null,824]
[{"$f":"\"The probability is \"&TEXT($B$17,\"0%\")&\" that our Xbar lies with in +/- 2 standard deviations (Standard Error because it is the SDOXbar)\"","v":"The probability is 95% that our Xbar lies with in +/- 2 standard deviations (Standard Error because it is the SDOXbar)"},null,null,null,null,null,null,null,null,424]
[{"$f":"\"Our Xbar of \"&DOLLAR(B13)&\" is outside our interval and because the chances of this are so small (\"&TEXT(1-B17,\"0%\")&\"), we say that it\"","v":"Our Xbar of $850.00 is outside our interval and because the chances of this are so small (5%), we say that it"},null,null,null,null,null,null,null,null,962]
[{"$f":"\"does not seem reasonable that we could have taken a sample and gotten \"&DOLLAR(B13)&\". Our sampling error is not acceptable.\"","v":"does not seem reasonable that we could have taken a sample and gotten $850.00. Our sampling error is not acceptable."},null,null,null,null,null,null,null,null,1002]
[{"$f":"\"We are \"&TEXT(B17,\"0%\")&\" sure that the original claim of \"&DOLLAR(B7)&\" does not seem reasonable.\"","v":"We are 95% sure that the original claim of $822.00 does not seem reasonable."},null,null,null,null,null,null,null,null,926]
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{"sheet":"Sigma Known","index":2,"n_rows":305,"n_cols":10,"rows_kept":305,"cut":false,"hidden":false,"merged":[]}
["An insurance company would like to estimate the average amount paid per year for an insurance policy. They have past data that can"]
["provide a good estimate of the population standard deviation."]
["Create an 95% confidence interval so that the company has a range of values to estimate the unknown population mean."]
[]
["Sample Annual Insurance Fees",null,"n",null," =COUNT(A6:A305)",null,null,null,null,716]
[938,null,"Xbar",null," =AVERAGE(A6:A305)",null,null,null,null,926]
[601,null,"Sigma",202]
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[390,null,"Confidence Level",0.95,null,"How sure we are that pop mean is in interval"]
[733,null,"Alpha",null," =1-D9","How sure we are that pop mean is NOT in interval. Risk we take that Pop Mean is not in interval"]
[1074,null,"Alpha/2",null," =D10/2","Prob. In upper or lower tail"]
[988]
[759,null,"Method 1:"]
[776,null,"NORM.INV Method"]
[1020,null,"Lower Limit",null," =NORM.INV(D11,D6,D8)",null," =NORM.INV(Alpha/2,Xbar,Standard Error)"]
[1074,null,"Upper Limit",null," =NORM.INV(1-D11,D6,D8)",null," =NORM.INV(1-Alpha/2,Xbar,Standard Error)"]
[927]
[1100,null,"Method 2:"]
[1220,null,"NORM.S.INV Method"]
[1002,null,"Z Associated with upper Alpha/2",null," =NORM.S.INV(1-D11)",null," =NORM.S.INV(1-Alpha/2)"]
[843,null,"Margin of Error = Alpha/2 * Standard Error",null," =D8*D20"]
[852,null,"Lower Limit",null," =D6-D21"]
[926,null,"Upper Limit",null," =D6+D21"]
[806]
[980,null,"Method 3:"]
[703,null,"CONFIDENCE.NORM Method"]
[793,null,"Margin of Error",null," =CONFIDENCE.NORM(D10,D7,D5)",null," =CONFIDENCE.NORM(Alpha,Sigma,Sample Size)"]
[774,null,"Lower Limit",null," =D6-D27"]
[1135,null,"Upper Limit",null," =D6+D27"]
[717,null,{"$f":"IF(D29=\"\",\"\",\"Our \"&TEXT($D$9,\"0%\")&\" Confidence Interval has limits of \"&ROUND($D$28,2)&\" and \"&ROUND($D$29,2)&\". We are about \"&TEXT($D$9,\"0%\")&\" sure that the population mean will lie within this interval. We are about \"&TEXT(1-$D$9,\"0%\")&\" sure that the population mean will NOT lie within this interval. \")","v":""}]
[872,null,{"$f":"IF(D29=\"\",\"\",\"If we were to construct 100 similar intervals we would expect \"&D9*100&\" to contain the population mean and \"&(1-D9)*100&\" to NOT contain the population mean.\")","v":""}]
[979,null,{"$f":"IF(D29=\"\",\"\",\"We estimate the population mean to be about \"&ROUND(D6,2)&\" with a margin of error of +/- \"&ROUND(D27,2)&\".\")","v":""}]
[870,null,{"$f":"IF(D29=\"\",\"\",\"A reasonable range of values for the population mean is \"&ROUND($D$28,2)&\" to \"&ROUND($D$29,2)&\".\")","v":""}]
[873,null,{"$f":"IF(D29=\"\",\"\",\"We are \"&TEXT($D$9,\"0%\")&\" sure that the pop mean for annual insurance cost is between \"&DOLLAR($D$28,2)&\" and \"&DOLLAR($D$29,2)&\".\")","v":""}]
[996]
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[860,null,"Sample Mean = Xbar =",850]
[824,null,"Lower Limit",null," =D39-D38"]
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[905,null,{"$f":"\"We are \"&TEXT($D$9,\"0%\")&\" sure that the pop mean for annual insurance cost is between \"&DOLLAR(D40,2)&\" and \"&DOLLAR(D41,2)&\".\"","v":"We are 95% sure that the pop mean for annual insurance cost is between $0.00 and $0.00."}]
[879,null,"Notice, that if it turned out that we could calculate the pop mean ($822), we would see that our Pop"]
[395,null,"Mean is not in our interval. This would be the 5% situation where our interval would not contain the"]
[926,null,"Pop Mean. How big should you make the interval, then?"]
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{"sheet":"Sigma Known(an)","index":3,"n_rows":305,"n_cols":10,"rows_kept":305,"cut":false,"hidden":false,"merged":[]}
["An insurance company would like to estimate the average amount paid per year for an insurance policy. They have past data that can"]
["provide a good estimate of the population standard deviation."]
["Create an 95% confidence interval so that the company has a range of values to estimate the unknown population mean."]
[]
["Sample Annual Insurance Fees",null,"n",{"$f":"COUNT(A6:A305)","v":300}," =COUNT(A6:A305)",null,null,null,null,716]
[938,null,"Xbar",{"$f":"AVERAGE(A6:A305)","v":837.20666666666671}," =AVERAGE(A6:A305)",null,null,null,null,926]
[601,null,"Sigma",202]
[988,null,"Standard Error of Mean =Sigma/SQRT(n)",{"$f":"D7/SQRT(D5)","v":11.662475437630439}," =D7/SQRT(D5)","Standard Deviation of Sampling Distribution of Xbar"]
[390,null,"Confidence Level",0.95,null,"How sure we are that pop mean is in interval"]
[733,null,"Alpha",{"$f":"1-D9","v":5.0000000000000044E-2}," =1-D9","How sure we are that pop mean is NOT in interval. Risk we take that Pop Mean is not in interval"]
[1074,null,"Alpha/2",{"$f":"D10/2","v":2.5000000000000022E-2}," =D10/2","Prob. In upper or lower tail"]
[988]
[759,null,"Method 1:"]
[776,null,"NORM.INV Method"]
[1020,null,"Lower Limit",{"$f":"_xlfn.NORM.INV(D11,D6,D8)","v":814.34863483832805}," =NORM.INV(D11,D6,D8)",null," =NORM.INV(Alpha/2,Xbar,Standard Error)"]
[1074,null,"Upper Limit",{"$f":"_xlfn.NORM.INV(1-D11,D6,D8)","v":860.06469849500536}," =NORM.INV(1-D11,D6,D8)",null," =NORM.INV(1-Alpha/2,Xbar,Standard Error)"]
[927]
[1100,null,"Method 2:"]
[1220,null,"NORM.S.INV Method"]
[1002,null,"Z Associated with upper Alpha/2",{"$f":"_xlfn.NORM.S.INV(1-D11)","v":1.9599639845400536}," =NORM.S.INV(1-D11)",null," =NORM.S.INV(1-Alpha/2)"]
[843,null,"Margin of Error = Alpha/2 * Standard Error",{"$f":"D20*D8","v":22.85803182833866}," =D8*D20"]
[852,null,"Lower Limit",{"$f":"D6-D21","v":814.34863483832805}," =D6-D21"]
[926,null,"Upper Limit",{"$f":"D6+D21","v":860.06469849500536}," =D6+D21"]
[806]
[980,null,"Method 3:"]
[703,null,"CONFIDENCE.NORM Method"]
[793,null,"Margin of Error",{"$f":"_xlfn.CONFIDENCE.NORM(D10,D7,D5)","v":22.85803182833866}," =CONFIDENCE.NORM(D10,D7,D5)",null," =CONFIDENCE.NORM(Alpha,Sigma,Sample Size)"]
[774,null,"Lower Limit",{"$f":"D6-D27","v":814.34863483832805}," =D6-D27"]
[1135,null,"Upper Limit",{"$f":"D6+D27","v":860.06469849500536}," =D6+D27"]
[717,null,{"$f":"IF(D29=\"\",\"\",\"Our \"&TEXT($D$9,\"0%\")&\" Confidence Interval has limits of \"&ROUND($D$28,2)&\" and \"&ROUND($D$29,2)&\". We are about \"&TEXT($D$9,\"0%\")&\" sure that the population mean will lie within this interval. We are about \"&TEXT(1-$D$9,\"0%\")&\" sure that the population mean will NOT lie within this interval. \")","v":"Our 95% Confidence Interval has limits of 814.35 and 860.06. We are about 95% sure that the population mean will lie within this interval. We are about 5% sure that the population mean will NOT lie within this interval. "}]
[872,null,{"$f":"IF(D29=\"\",\"\",\"If we were to construct 100 similar intervals we would expect \"&D9*100&\" to contain the population mean and \"&(1-D9)*100&\" to NOT contain the population mean.\")","v":"If we were to construct 100 similar intervals we would expect 95 to contain the population mean and 5 to NOT contain the population mean."}]
[979,null,{"$f":"IF(D29=\"\",\"\",\"We estimate the population mean to be about \"&ROUND(D6,2)&\" with a margin of error of +/- \"&ROUND(D27,2)&\".\")","v":"We estimate the population mean to be about 837.21 with a margin of error of +/- 22.86."}]
[870,null,{"$f":"IF(D29=\"\",\"\",\"A reasonable range of values for the population mean is \"&ROUND($D$28,2)&\" to \"&ROUND($D$29,2)&\".\")","v":"A reasonable range of values for the population mean is 814.35 to 860.06."}]
[873,null,{"$f":"IF(D29=\"\",\"\",\"We are \"&TEXT($D$9,\"0%\")&\" sure that the pop mean for annual insurance cost is between \"&DOLLAR($D$28,2)&\" and \"&DOLLAR($D$29,2)&\".\")","v":"We are 95% sure that the pop mean for annual insurance cost is between $814.35 and $860.06."}]
[996]
[716,null,"Method 3:"]
[722,null,"CONFIDENCE.NORM Method"]
[769,null,"Margin of Error",{"$f":"_xlfn.CONFIDENCE.NORM(1-D9,D7,COUNT(A6:A305))","v":22.85803182833866}," =CONFIDENCE.NORM(D10,D7,D5)",null," =CONFIDENCE.NORM(Alpha,Sigma,Sample Size)"]
[860,null,"Sample Mean = Xbar =",850]
[824,null,"Lower Limit",{"$f":"D39-D38","v":827.14196817166135}," =D39-D38"]
[824,null,"Upper Limit",{"$f":"D39+D38","v":872.85803182833865}," =D39+D38"]
[905,null,{"$f":"\"We are \"&TEXT($D$9,\"0%\")&\" sure that the pop mean for annual insurance cost is between \"&DOLLAR(D40,2)&\" and \"&DOLLAR(D41,2)&\".\"","v":"We are 95% sure that the pop mean for annual insurance cost is between $827.14 and $872.86."}]
[879,null,"Notice, that if it turned out that we could calculate the pop mean ($822), we would see that our Pop"]
[395,null,"Mean is not in our interval. This would be the 5% situation where our interval would not contain the"]
[926,null,"Pop Mean. How big should you make the interval, then?"]
[816]
[873]
[686]
[722]
[722]
[835]
[436]
[843,null,null,"Skew",{"$f":"SKEW(A6:A305)","v":-0.3303148141217756}]
[775,null,null,"Max",{"$f":"MAX(A6:A305)","v":1268}]
[824,null,null,"Min",{"$f":"MIN(A6:A305)","v":249}]
[824,null,null,"Range",{"$f":"E54-E55","v":1019}]
[1110,null,null,"Start",0]
[824,null,null,"Increment",100]
[1074]
[988,null,null,"Low","High","Frequency"]
[1010,null,null,{"$f":"E57","v":0},{"$f":"D61+$E$58","v":100},{"$f":"COUNTIFS($A$6:$A$305,\">=\"&D61,$A$6:$A$305,\"<=\"&E61)","v":0}]
[775,null,null,{"$f":"E61","v":100},200,{"$f":"COUNTIFS($A$6:$A$305,\">=\"&D62,$A$6:$A$305,\"<=\"&E62)","v":0}]
[988,null,null,{"$f":"E62","v":200},300,1]
[926,null,null,300,400,3]
[722,null,null,400,500,9]
[824,null,null,500,600,13]
[715,null,null,600,700,23]
[760,null,null,700,800,70]
[988,null,null,800,900,75]
[967,null,null,900,1000,57]
[652,null,null,1000,1100,39]
[736,null,null,1100,1200,8]
[557,null,null,1200,1300,4]
[1074]
[626]
[775]
[722]
[939]
[826]
[476]
[481]
[905]
[824]
[819]
[687]
[1074]
[705]
[502,null,null,"Mew","Xbar","P(Xbar)"]
[926,null,null,null,21.8,null,null,null,21.8]
[884,null,null,null,21.900000000000002,null,null,null,28.1]
[915,null,null,null,22]
[709,null,null,null,22.1]
[824,null,null,null,22.2]
[722,null,null,null,22.3]
[1064,null,null,null,22.400000000000002]
[988,null,null,null,22.5]
[745,null,null,null,22.6]
[867,null,null,null,22.7]
[926,null,null,null,22.8]
[673,null,null,null,22.900000000000002]
[1021,null,null,null,23]
[618,null,null,null,23.1]
[758,null,null,null,23.2]
[824,null,null,null,23.3]
[824,null,null,null,23.400000000000002]
[753,null,null,null,23.5]
[873,null,null,null,23.6]
[716,null,null,null,23.7]
[622,null,null,null,23.8]
[1074,null,null,null,23.900000000000002]
[873,null,null,null,24]
[873,null,null,null,24.1]
[715,null,null,null,24.200000000000003]
[501,null,null,null,24.3]
[838,null,null,null,24.400000000000002]
[605,null,null,null,24.5]
[675,null,null,null,24.6]
[926,null,null,null,24.700000000000003]
[761,null,null,null,24.8]
[926,null,null,null,24.900000000000002]
[988,null,null,null,25]
[873,null,null,null,25.1]
[722,null,null,null,25.200000000000003]
[775,null,null,null,25.3]
[1268,null,null,null,25.400000000000002]
[778,null,null,null,25.5]
[956,null,null,null,25.6]
[895,null,null,null,25.700000000000003]
[460,null,null,null,25.8]
[722,null,null,null,25.900000000000002]
[925,null,null,null,26]
[771,null,null,null,26.1]
[1074,null,null,null,26.200000000000003]
[906,null,null,null,26.3]
[926,null,null,null,26.400000000000002]
[739,null,null,null,26.5]
[988,null,null,null,26.6]
[873,null,null,null,26.700000000000003]
[390,null,null,null,26.8]
[926,null,null,null,26.900000000000002]
[1189,null,null,null,27]
[1074,null,null,null,27.1]
[420,null,null,null,27.200000000000003]
[805,null,null,null,27.3]
[873,null,null,null,27.400000000000002]
[891,null,null,null,27.5]
[988,null,null,null,27.6]
[773,null,null,null,27.700000000000003]
[1074,null,null,null,27.8]
[424,null,null,null,27.900000000000002]
[722,null,null,null,28]
[894,null,null,null,28.1]
[1074]
[528]
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["n = ",100,null,"n = ",5]
["df = ",{"$f":"B1-1","v":99},null,"df = ",{"$f":"E1-1","v":4}]
["Confidence Level",0.95,null,"Confidence Level",0.95]
["T-value Upper",{"$f":"_xlfn.T.INV.2T(1-B3,B1)","v":1.98397151852355},null,"T-value Upper",{"$f":"_xlfn.T.INV.2T(1-E3,E1)","v":2.570581835636315}]
[]
["t",{"$f":"A1&B1&CHAR(10)&A2&B2","v":"n = 100\ndf = 99"},null,"t",{"$f":"D1&E1&CHAR(10)&D2&E2","v":"n = 5\ndf = 4"}]
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[2.0499999999999998,4.9780839694463994E-2,null,2.0499999999999998,6.2275274196749469E-2]
[2.0600000000000005,4.8799585576007817E-2,null,2.0600000000000005,6.1501961860973037E-2]
[2.0700000000000003,4.7833421042510246E-2,null,2.0700000000000003,6.073836108400979E-2]
[2.08,4.6882222556591469E-2,null,2.08,5.9984365545804941E-2]
[2.09,4.5945864790626061E-2,null,2.09,5.9239869407081383E-2]
[2.1000000000000005,4.5024220714599397E-2,null,2.1000000000000005,5.8504767334097138E-2]
[2.1100000000000003,4.411716168288847E-2,null,2.1100000000000003,5.7778954522225069E-2]
[2.12,4.3224557519936431E-2,null,2.12,5.7062326718385313E-2]
[2.13,{"$f":"_xlfn.T.DIST(A520,B$2,0)","v":4.234627660479641E-2},null,{"$f":"A520","v":2.13},{"$f":"_xlfn.T.DIST(D520,E$2,0)","v":5.6354780242364219E-2}]
[2.1399999999999997,4.1482185954517553E-2,null,2.1399999999999997,5.5656212007050058E-2]
[2.1500000000000004,4.0632151306350131E-2,null,2.1500000000000004,5.4966519537616901E-2]
[2.16,3.9796037198746928E-2,null,2.16,5.4285600989687245E-2]
[2.17,3.8973707051138902E-2,null,2.17,5.3613355166502584E-2]
[2.1799999999999997,3.8165023242466997E-2,null,2.1799999999999997,5.2949681535132541E-2]
[2.1900000000000004,3.7369847188449559E-2,null,2.1900000000000004,5.2294480241750339E-2]
[2.2000000000000002,3.6588039417569954E-2,null,2.2000000000000002,5.1647652126004202E-2]
[2.21,3.5819459645766813E-2,null,2.21,5.1009098734510538E-2]
[2.2199999999999998,3.506396684981386E-2,null,2.2199999999999998,5.0378722333498861E-2]
[2.2300000000000004,3.4321419339375048E-2,null,2.2300000000000004,4.9756425920633042E-2]
[2.2400000000000002,3.3591674827723253E-2,null,2.2400000000000002,4.9142113236036289E-2]
[2.25,3.287459050111146E-2,null,2.25,4.853568877254489E-2]
[2.2599999999999998,3.2170023086787215E-2,null,2.2599999999999998,4.7937057785216668E-2]
[2.2700000000000005,3.1477828919641515E-2,null,2.2700000000000005,4.7346126300117829E-2]
[2.2800000000000002,3.0797864007485378E-2,null,2.2800000000000002,4.6762801122413586E-2]
[2.29,3.0129984094947045E-2,null,2.29,4.6186989843784193E-2]
[2.2999999999999998,2.9474044725985849E-2,null,2.2999999999999998,4.5618600849191629E-2]
[2.3100000000000005,2.8829901305018241E-2,null,2.3100000000000005,4.5057543323017847E-2]
[2.3200000000000003,2.8197409156653391E-2,null,2.3200000000000003,4.450372725459735E-2]
[2.33,2.7576423584036069E-2,null,2.33,4.3957063443165037E-2]
[2.34,2.6966799925796987E-2,null,2.34,4.3417463502240974E-2]
[2.3500000000000005,2.6368393611609746E-2,null,2.3500000000000005,4.2884839863471802E-2]
[2.3600000000000003,2.578106021635675E-2,null,2.3600000000000003,4.2359105779949363E-2]
[2.37,2.5204655512904746E-2,null,2.37,4.1840175329025342E-2]
[2.38,2.4639035523494737E-2,null,2.38,4.132796341464158E-2]
[2.3899999999999997,2.4084056569748959E-2,null,2.3899999999999997,4.0822385769193982E-2]
[2.4000000000000004,2.3539575321300271E-2,null,2.4000000000000004,4.0323358954948235E-2]
[2.41,2.300544884304984E-2,null,2.41,3.9830800365025065E-2]
[2.42,2.2481534641058711E-2,null,2.42,3.9344628223971313E-2]
[2.4299999999999997,2.1967690707081895E-2,null,2.4299999999999997,3.8864761587934761E-2]
[2.4400000000000004,2.1463775561751604E-2,null,2.4400000000000004,3.8391120344457193E-2]
[2.4500000000000002,2.0969648296419809E-2,null,2.4500000000000002,3.7923625211903102E-2]
[2.46,2.0485168613668028E-2,null,2.46,3.7462197738537754E-2]
[2.4699999999999998,2.0010196866495904E-2,null,2.4699999999999998,3.7006760301270626E-2]
[2.4800000000000004,1.9544594096198763E-2,null,2.4800000000000004,3.6557236104077899E-2]
[2.4900000000000002,1.9088222068945646E-2,null,2.4900000000000002,3.6113549176118476E-2]
[2.5,1.8640943311069597E-2,null,2.5,3.5675624369556645E-2]
[2.5099999999999998,1.8202621143083669E-2,null,2.5099999999999998,3.5243387357105062E-2]
[2.5200000000000005,1.777311971243482E-2,null,2.5200000000000005,3.4816764629300501E-2]
[2.5300000000000002,1.7352304025010337E-2,null,2.5300000000000002,3.4395683491525095E-2]
[2.54,1.6940039975410041E-2,null,2.54,3.3980072060784579E-2]
[2.5499999999999998,1.6536194375999916E-2,null,2.5499999999999998,3.3569859262255974E-2]
[2.5600000000000005,1.6140634984761672E-2,null,2.5600000000000005,3.3164974825615423E-2]
[2.5700000000000003,1.5753230531954088E-2,null,2.5700000000000003,3.2765349281157367E-2]
[2.58,1.5373850745601833E-2,null,2.58,3.237091395571555E-2]
[2.59,1.5002366375828512E-2,null,2.59,3.1981600968396522E-2]
[2.6000000000000005,1.4638649218050357E-2,null,2.6000000000000005,3.1597343226134868E-2]
[2.6100000000000003,1.4282572135047737E-2,null,2.6100000000000003,3.1218074419080904E-2]
[2.62,1.3934009077931596E-2,null,2.62,3.0843729015828714E-2]
[2.63,1.3592835106022836E-2,null,2.63,3.0474242258494863E-2]
[2.6399999999999997,1.3258926405662235E-2,null,2.6399999999999997,3.0109550157655728E-2]
[2.6500000000000004,1.29321603079692E-2,null,2.6500000000000004,2.9749589487152187E-2]
[2.66,1.2612415305567707E-2,null,2.66,2.9394297778769663E-2]
[2.67,1.2299571068297776E-2,null,2.67,2.9043613316801324E-2]
[2.6799999999999997,1.1993508457931575E-2,null,2.6799999999999997,2.8697475132502204E-2]
[2.6900000000000004,1.1694109541912866E-2,null,2.6900000000000004,2.8355822998441475E-2]
[2.7,1.1401257606138906E-2,null,2.7,2.8018597422760021E-2]
[2.71,1.1114837166803686E-2,null,2.71,2.7685739643339743E-2]
[2.7199999999999998,1.0834733981322359E-2,null,2.7199999999999998,2.7357191621891857E-2]
[2.7300000000000004,1.0560835058355592E-2,null,2.7300000000000004,2.7032896037969701E-2]
[2.74,1.0293028666953807E-2,null,2.74,2.6712796282913082E-2]
[2.75,1.0031204344840221E-2,null,2.75,2.6396836453728884E-2]
[2.76,9.7752529058527174E-3,null,2.76,2.6084961346914837E-2]
[2.7700000000000005,{"$f":"_xlfn.T.DIST(A584,B$2,0)","v":9.525066446563743E-3},null,{"$f":"A584","v":2.7700000000000005},{"$f":"_xlfn.T.DIST(D584,E$2,0)","v":2.5777116452230912E-2}]
[2.7800000000000002,9.2805383520979303E-3,null,2.7800000000000002,2.5473247946424117E-2]
[2.79,9.0415633011666618E-3,null,2.79,2.5173302686911436E-2]
[2.8,8.8080372703395211E-3,null,2.8,2.4877228205426087E-2]
[2.8100000000000005,8.57985753757152E-3,null,2.8100000000000005,2.458497270163126E-2]
[2.8200000000000003,8.3569226850060321E-3,null,2.8200000000000003,2.4296485036706474E-2]
[2.83,8.1391326010721333E-3,null,2.83,2.4011714726909945E-2]
[2.84,7.926388481896111E-3,null,2.84,2.3730611937122111E-2]
[2.8500000000000005,7.7185928320458617E-3,null,2.8500000000000005,2.3453127474373323E-2]
[2.8600000000000003,7.515649464627446E-3,null,2.8600000000000003,2.3179212781360238E-2]
[2.87,7.3174635007524748E-3,null,2.87,2.2908819929953871E-2]
[2.88,7.123941368395191E-3,null,2.88,2.2641901614703364E-2]
[2.8899999999999997,6.9349908006579031E-3,null,2.8899999999999997,2.2378411146338425E-2]
[2.9000000000000004,6.7505208334630159E-3,null,2.9000000000000004,2.2118302445273696E-2]
[2.91,6.5704418026902743E-3,null,2.91,2.186153003511828E-2]
[2.92,6.3946653407768927E-3,null,2.92,2.1608049036192945E-2]
[2.9299999999999997,6.2231043727989472E-3,null,2.9299999999999997,2.1357815159058106E-2]
[2.9400000000000004,6.0556731120515149E-3,null,2.9400000000000004,2.1110784698055208E-2]
[2.95,5.8922870551451675E-3,null,2.95,2.0866914524863871E-2]
[2.96,5.7328629766360767E-3,null,2.96,2.0626162082077182E-2]
[2.9699999999999998,5.5773189232070754E-3,null,2.9699999999999998,2.0388485376797709E-2]
[2.9800000000000004,5.425574207416275E-3,null,2.9800000000000004,2.0153842974256049E-2]
[2.99,5.2775494010302657E-3,null,2.99,1.9922193991454406E-2]
[3,{"$f":"_xlfn.T.DIST(A607,B$2,0)","v":5.1331663279579201E-3},null,3,{"$f":"_xlfn.T.DIST(D607,E$2,0)","v":1.9693498090836536E-2}]

{"sheet":"Sigma Not Known","index":5,"n_rows":22,"n_cols":7,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
["Sample # Pages From Cartridge",null,"Printers Manufacturers is a manufacturer of computer printers and printer"]
[1907,null,"cartridges. They would like to create an ad that says how many pages a"]
[2501,null,"customer could expect from the cartridge."]
[2258,null,"Something like: \"A customer can expect an average of XXX within the margin"]
[2410,null,"of error of XXX.\""]
[2942]
[2455,null,"X bar (pages)",null,null,null," =ROUND(AVERAGE(A2:A11),0)"]
[2058,null,"s (pages)",null,null,null," =ROUND(STDEV.S(A2:A11),0)"]
[2298,null,"n",null,null,null," =COUNT(A2:A11)"]
[2751,null,"# of samples",1]
[2508,null,"df",null,null,null," =D9-D10"]
[null,null,"Standard Error",null,null,null," =D8/SQRT(D9)"]
[null,null,"Confidence Level",0.95]
[null,null,"Alpha",null,null,null," =1-D13"]
[null,null,"Alpha/2",null,null,null," =D14/2"]
[null,null,"t",null,null,null," =T.INV(1-D15,D11)"]
[null,null,"Margin of error",null,null,"Method 1"," =D16*D12"]
[null,null,"Margin of error",null,null,"Method 2"," =CONFIDENCE.T(D14,D8,D9)"]
[null,null,"lower Xbar",null,null,null," =$D$7-$D$18"]
[null,null,"upper Xbar",null,null,null," =$D$7+$D$18"]
[]
[null,null,null,null,null,"Method 3"]

{"sheet":"Sigma Not Known(an)","index":6,"n_rows":44,"n_cols":7,"rows_kept":44,"cut":false,"hidden":false,"merged":[]}
["Sample # Pages From Cartridge",null,"Printers Manufacturers is a manufacturer of computer printers and printer"]
[1907,null,"cartridges. They would like to create an ad that says how many pages a"]
[2501,null,"customer could expect from the cartridge."]
[2258,null,"Something like: \"A customer can expect an average of XXX within the margin"]
[2410,null,"of error of XXX.\""]
[2942]
[2455,null,"X bar (pages)",{"$f":"ROUND(AVERAGE(A2:A11),0)","v":2409},null,null," =ROUND(AVERAGE(A2:A11),0)"]
[2058,null,"s (pages)",{"$f":"ROUND(_xlfn.STDEV.S(A2:A11),0)","v":304},null,null," =ROUND(STDEV.S(A2:A11),0)"]
[2298,null,"n",{"$f":"COUNT(A2:A11)","v":10},null,null," =COUNT(A2:A11)"]
[2751,null,"# of samples",1]
[2508,null,"df",{"$f":"D9-D10","v":9},null,null," =D9-D10"]
[null,null,"Standard Error",{"$f":"D8/SQRT(D9)","v":96.133240869118723},null,null," =D8/SQRT(D9)"]
[null,null,"Confidence Level",0.95]
[null,null,"Alpha",{"$f":"1-D13","v":5.0000000000000044E-2},null,null," =1-D13"]
[null,null,"Alpha/2",{"$f":"D14/2","v":2.5000000000000022E-2},null,null," =D14/2"]
[null,null,"t",{"$f":"_xlfn.T.INV(1-D15,D11)","v":2.2621571627982049},null,null," =T.INV(1-D15,D11)"]
[null,null,"Margin of error",{"$f":"ROUND(D12*D16,0)","v":217},null,"Method 1"," =D16*D12"]
[null,null,"Margin of error",{"$f":"ROUND(_xlfn.CONFIDENCE.T(D14,D8,D9),0)","v":217},null,"Method 2"," =CONFIDENCE.T(D14,D8,D9)"]
[null,null,"lower Xbar",{"$f":"D7-D17","v":2192},null,null," =$D$7-$D$18"]
[null,null,"upper Xbar",{"$f":"D7+D18","v":2626},null,null," =$D$7+$D$18"]
[]
[null,null,null,null,null,"Method 3"]
[null,null,"Sample # Pages From Cartridge"]
[]
[null,null,"Mean",2408.8000000000002]
[null,null,"Standard Error",96.134257970588038]
[null,null,"Median",2432.5]
[null,null,"Mode",{"$error":"#N/A"}]
[null,null,"Standard Deviation",304.00321635725453]
[null,null,"Sample Variance",92417.955555555716]
[null,null,"Kurtosis",0.1052419625105161]
[null,null,"Skewness",9.4946322263048152E-2]
[null,null,"Range",1035]
[null,null,"Minimum",1907]
[null,null,"Maximum",2942]
[null,null,"Sum",24088]
[null,null,"Count",10]
[null,null,"Confidence Level(95.0%)",217.47080025845614]
[]
[null,null,"Lower Limit",{"$f":"D25-D38","v":2191.329199741544}]
[null,null,"Upper Limit",{"$f":"D25+D38","v":2626.2708002584563}]
[]
[null,null,"A customer can expect an average of 2409 pages within the margin"]
[null,null,"of error of 217 pages"]

{"sheet":"T(2)","index":7,"n_rows":54,"n_cols":7,"rows_kept":54,"cut":false,"hidden":false,"merged":[]}
["Restaurant Magazine wants to rate a particular restaurant. They go out and ask 50 randomly selected customers to give"]
["a rating between 1 and 10 so they can estimate the population mean rating."]
[]
["1-10 Rating of Resturant",null,"n",null," =COUNT(A5:A54)"]
[6,null,"df",null," =D4-1","Degrees of Freedom = n - # of samples"]
[10,null,"Xbar",null," =AVERAGE(A5:A54)"]
[4,null,"s",null," =STDEV.S(A5:A54)"]
[10,null,"Standard Error of Mean =s/SQRT(n)",null," =D7/SQRT(D4)","SE = Standard Deviation of Sampling Distribution of Xbar"]
[5,null,"Confidence Level",0.95,null,"How sure we are that pop mean is in interval"]
[2,null,"Alpha",null," =1-D9","How sure we are that pop mean is NOT in interval. Risk we take that Pop Mean is not in interval"]
[8,null,"Alpha/2",null," =D10/2","Prob. In upper or lower tail"]
[3]
[2,null,"Method 1:"]
[7,null,"T.INV Method"]
[5,null,"Upper t",null," =T.INV(1-D11,D5)",null," =T.INV(1-alpha/2,df)"]
[6,null,"Margin of Error",null," =D15*D8",null," =t * SE"]
[8,null,"Lower Limit",null," =D6-D16",null," =Xbar - Margin of Error"]
[2,null,"Upper Limit",null," =D6+D16",null," =Xbar + Margin of Error"]
[8]
[7,null,"Method 2:"]
[6,null,"CONFIDENCE.T Method"]
[8,null,"Margin of Error",null," =CONFIDENCE.T(D10,D7,D4)",null," =CONFIDENCE.T(alpha,s,n)"]
[9,null,"Lower Limit",null," =D6-D22",null," =Xbar - Margin of Error"]
[7,null,"Upper Limit",null," =D6+D22",null," =Xbar + Margin of Error"]
[2]
[9,null,"Method 3:"]
[9,null,"Data Analysis, Descriptive Statistics Method",null,null,null,"Data Ribbon Tab, Analysis Group, Data Analysis button, Descriptive Statistics"]
[6]
[5,null,"1-10 Rating of Resturant"]
[8]
[2,null,"Mean",5.98]
[5,null,"Standard Error",0.35741703761224114]
[3,null,"Median",6]
[9,null,"Mode",2]
[8,null,"Standard Deviation",2.5273201100722305]
[9,null,"Sample Variance",6.3873469387755106]
[9,null,"Kurtosis",-1.0728055578009994]
[6,null,"Skewness",-0.30844475361852403]
[5,null,"Range",8]
[2,null,"Minimum",2]
[5,null,"Maximum",10]
[6,null,"Sum",299]
[9,null,"Count",50]
[7,null,"Confidence Level(95.0%)",0.71825642811364954]
[9,null,"Lower Limit",{"$f":"D31-D44","v":5.2617435718863508}," =D30-D43",null," =Xbar - Margin of Error"]
[7,null,"Upper Limit",{"$f":"D31+D44","v":6.6982564281136501}," =D30+D43",null," =Xbar + Margin of Error"]
[2,null,{"$f":"\"Our \"&TEXT($D$9,\"0%\")&\" Confidence Interval has limits of \"&ROUND(D45,1)&\" and \"&ROUND(D46,1)&\". We are about \"&TEXT($D$9,\"0%\")&\" sure that the population mean will lie within this interval. We are about \"&TEXT(1-$D$9,\"0%\")&\" sure that the population mean will NOT lie within this interval. \"","v":"Our 95% Confidence Interval has limits of 5.3 and 6.7. We are about 95% sure that the population mean will lie within this interval. We are about 5% sure that the population mean will NOT lie within this interval. "}]
[2,null,{"$f":"\"If we were to construct 100 similar intervals we would expect \"&D9*100&\" to contain the population mean and \"&(1-D9)*100&\" to NOT contain the population mean.\"","v":"If we were to construct 100 similar intervals we would expect 95 to contain the population mean and 5 to NOT contain the population mean."}]
[7,null,{"$f":"\"We estimate the population mean for rating is about \"&ROUND(D6,1)&\" with a margin of error of +/- \"&ROUND(D43,1)&\".\"","v":"We estimate the population mean for rating is about 0 with a margin of error of +/- 50."}]
[5,null,{"$f":"\"A reasonable range of values for the population mean is \"&ROUND(D45,1)&\" to \"&ROUND(D46,1)&\".\"","v":"A reasonable range of values for the population mean is 5.3 to 6.7."}]
[4,null,{"$f":"\"We are \"&TEXT($D$9,\"0%\")&\" sure that the pop mean for the resturant rating is between \"&ROUND(D45,1)&\" and \"&ROUND(D46,1)&\".\"","v":"We are 95% sure that the pop mean for the resturant rating is between 5.3 and 6.7."}]
[7]
[2]
[7]

{"sheet":"T(2an)","index":8,"n_rows":54,"n_cols":7,"rows_kept":54,"cut":false,"hidden":false,"merged":[]}
["Restaurant Magazine wants to rate a particular restaurant. They go out and ask 50 randomly selected customers to give"]
["a rating between 1 and 10 so they can estimate the population mean rating."]
[]
["1-10 Rating of Resturant",null,"n",{"$f":"COUNT(A5:A54)","v":50}," =COUNT(A5:A54)"]
[6,null,"df",{"$f":"D4-1","v":49}," =D4-1","Degrees of Freedom = n - # of samples"]
[10,null,"Xbar",{"$f":"AVERAGE(A5:A54)","v":5.98}," =AVERAGE(A5:A54)"]
[4,null,"s",{"$f":"_xlfn.STDEV.S(A5:A54)","v":2.5273201100722305}," =STDEV.S(A5:A54)"]
[10,null,"Standard Error of Mean =s/SQRT(n)",{"$f":"D7/SQRT(D4)","v":0.35741703761224114}," =D7/SQRT(D4)","SE = Standard Deviation of Sampling Distribution of Xbar"]
[5,null,"Confidence Level",0.95,null,"How sure we are that pop mean is in interval"]
[2,null,"Alpha",{"$f":"1-D9","v":5.0000000000000044E-2}," =1-D9","How sure we are that pop mean is NOT in interval. Risk we take that Pop Mean is not in interval"]
[8,null,"Alpha/2",{"$f":"D10/2","v":2.5000000000000022E-2}," =D10/2","Prob. In upper or lower tail"]
[3]
[2,null,"Method 1:"]
[7,null,"T.INV Method"]
[5,null,"Upper t",{"$f":"_xlfn.T.INV(1-D11,D5)","v":2.0095752371292388}," =T.INV(1-D11,D5)",null," =T.INV(1-alpha/2,df)"]
[6,null,"Margin of Error",{"$f":"D15*D8","v":0.71825642811364954}," =D15*D8",null," =t * SE"]
[8,null,"Lower Limit",{"$f":"D6-D16","v":5.2617435718863508}," =D6-D16",null," =Xbar - Margin of Error"]
[2,null,"Upper Limit",{"$f":"D6+D16","v":6.6982564281136501}," =D6+D16",null," =Xbar + Margin of Error"]
[8]
[7,null,"Method 2:"]
[6,null,"CONFIDENCE.T Method"]
[8,null,"Margin of Error",{"$f":"_xlfn.CONFIDENCE.T(D10,D7,D4)","v":0.71825642811364954}," =CONFIDENCE.T(D10,D7,D4)",null," =CONFIDENCE.T(alpha,s,n)"]
[9,null,"Lower Limit",{"$f":"D6-D22","v":5.2617435718863508}," =D6-D22",null," =Xbar - Margin of Error"]
[7,null,"Upper Limit",{"$f":"D6+D22","v":6.6982564281136501}," =D6+D22",null," =Xbar + Margin of Error"]
[2]
[9,null,"Method 3:"]
[9,null,"Data Analysis, Descriptive Statistics Method",null,null,null,"Data Ribbon Tab, Analysis Group, Data Analysis button, Descriptive Statistics"]
[6,null,"1-10 Rating of Resturant"]
[5]
[8,null,"Mean",5.98]
[2,null,"Standard Error",0.35741703761224114]
[5,null,"Median",6]
[3,null,"Mode",2]
[9,null,"Standard Deviation",2.5273201100722305]
[8,null,"Sample Variance",6.3873469387755106]
[9,null,"Kurtosis",-1.0728055578009994]
[9,null,"Skewness",-0.30844475361852403]
[6,null,"Range",8]
[5,null,"Minimum",2]
[2,null,"Maximum",10]
[5,null,"Sum",299]
[6,null,"Count",50]
[9,null,"Confidence Level(95.0%)",0.71825642811364954]
[7]
[9,null,"Lower Limit",{"$f":"D30-D43","v":5.2617435718863508}," =D30-D43",null," =Xbar - Margin of Error"]
[7,null,"Upper Limit",{"$f":"D30+D43","v":6.6982564281136501}," =D30+D43",null," =Xbar + Margin of Error"]
[2,null,{"$f":"\"Our \"&TEXT($D$9,\"0%\")&\" Confidence Interval has limits of \"&ROUND(D45,1)&\" and \"&ROUND(D46,1)&\". We are about \"&TEXT($D$9,\"0%\")&\" sure that the population mean will lie within this interval. We are about \"&TEXT(1-$D$9,\"0%\")&\" sure that the population mean will NOT lie within this interval. \"","v":"Our 95% Confidence Interval has limits of 5.3 and 6.7. We are about 95% sure that the population mean will lie within this interval. We are about 5% sure that the population mean will NOT lie within this interval. "}]
[2,null,{"$f":"\"If we were to construct 100 similar intervals we would expect \"&D9*100&\" to contain the population mean and \"&(1-D9)*100&\" to NOT contain the population mean.\"","v":"If we were to construct 100 similar intervals we would expect 95 to contain the population mean and 5 to NOT contain the population mean."}]
[7,null,{"$f":"\"We estimate the population mean for rating is about \"&ROUND(D6,1)&\" with a margin of error of +/- \"&ROUND(D43,1)&\".\"","v":"We estimate the population mean for rating is about 6 with a margin of error of +/- 0.7."}]
[5,null,{"$f":"\"A reasonable range of values for the population mean is \"&ROUND(D45,1)&\" to \"&ROUND(D46,1)&\".\"","v":"A reasonable range of values for the population mean is 5.3 to 6.7."}]
[4,null,{"$f":"\"We are \"&TEXT($D$9,\"0%\")&\" sure that the pop mean for the resturant rating is between \"&ROUND(D45,1)&\" and \"&ROUND(D46,1)&\".\"","v":"We are 95% sure that the pop mean for the resturant rating is between 5.3 and 6.7."}]
[7]
[2]
[7]

{"sheet":"Pbar(1)","index":9,"n_rows":1109,"n_cols":8,"rows_kept":1109,"cut":false,"hidden":false,"merged":[]}
["Binomial Tests"]
["Experiment consists of a sequence of n identical trials. Random Variable counts the number of successes in a Fixed number of trials, n. - Fixed # of Identical Trials = n",null,null,null,null,"Yes"]
["Only 2 outcomes are possible on each identical trial. Success or Failure. - Each trial only results in S or F",null,null,null,null,"Yes"]
["Probability of Success = p = (π \"pi\"). Probability of Failure = 1-p. Probability remains the same on each trial. - p remains the same for each trial",null,null,null,null,"Yes"]
["The trials are independent (one does not affect the next) - All events are independent",null,null,null,null,"Yes"]
[]
["A large Seattle Coffee Company says that Excel skills are important for the 600 + employees that work in the Marketing and Accounting Department. A sample of potential employees who said they were knowledgeable with Excel is below."]
[]
["Response",null,"Sample Size = n",null,null,null,null," =COUNTA(A10:A1109)"]
["No",null,{"$f":"\"Count of \"&E10","v":"Count of Yes"},null,"Yes",null,null," =COUNTIF($A$10:$A$1109,F10)"]
["Yes",null,{"$f":"\"Count of \"&E11","v":"Count of No"},null,"No",null,null," =COUNTIF($A$10:$A$1109,F11)"]
["No",null,{"$f":"\"P(\"&E10&\")\"","v":"P(Yes)"},null,"sample proportion = Point Estimate","Pbar","Proportion of potential employees who say they know Excel well"," =D10/$D$9"]
["No",null,{"$f":"\"P(\"&E11&\")\"","v":"P(No)"},null,null,null,null," =D11/$D$9"]
["Yes",null,"n*p>5",null,{"$f":"IF(D14=\"\",\"\",D14>5)","v":""},"Can we use Normal Curve?",null," =D9*D12"]
["No",null,"n*(1-p)>5",null,{"$f":"IF(D15=\"\",\"\",D15>5)","v":""},null,null," =D9*D13"]
["No",null,"Confidence Level",0.95,null,null,null," 0.95"]
["No",null,"Significance Level",null,"alpha",null,null," =1-D16"]
["No",null,"alpha/2",null,null,null,null," =D17/2"]
["Yes",null,"z upper",null,null,"Method 2",null," =NORM.S.INV(1-D18)"]
["Yes",null,"Standard Error",null,"SQRT(p*(1-p)/n)",null,null," =SQRT(D12*D13/D9)"]
["No",null,"Margin of error",null,null,null,null," =D20*D19"]
["Yes",null,"Lower Limit",null,null,null,null," =$D$12-$D$21"]
["No",null,"Upper Limit",null,null,null,null," =$D$12+$D$21"]
["Yes",null,"Conclusion:"]
["No",null,{"$f":"IF(D23=\"\",\"\",\"The \"&TEXT(D16,\"0.00%\")&\" confidence interval for the \"&LOWER(G12)&\" is \"&TEXT(D22,\"0.0000\")&\" to \"&TEXT(D23,\"0.0000\")&\".\")","v":""}]
["Yes",null,{"$f":"IF(D23=\"\",\"\",\"So, since this company hires people on the spot if they know their field and they know Excel, be sure to study both in school!\")","v":""}]
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{"sheet":"Pbar(1an)","index":10,"n_rows":1109,"n_cols":9,"rows_kept":1109,"cut":false,"hidden":false,"merged":[]}
["Binomial Tests"]
["Experiment consists of a sequence of n identical trials. Random Variable counts the number of successes in a Fixed number of trials, n. - Fixed # of Identical Trials = n",null,null,null,null,"Yes"]
["Only 2 outcomes are possible on each identical trial. Success or Failure. - Each trial only results in S or F",null,null,null,null,"Yes"]
["Probability of Success = p = (π \"pi\"). Probability of Failure = 1-p. Probability remains the same on each trial. - p remains the same for each trial",null,null,null,null,"Yes"]
["The trials are independent (one does not affect the next) - All events are independent",null,null,null,null,"Yes"]
[]
["A large Seattle Coffee Company says that Excel skills are important for the 600 + employees that work in the Marketing and Accounting Department. A sample of potential employees who said they were knowledgeable with Excel is below."]
[]
["Response",null,"Sample Size = n",{"$f":"COUNTA(A10:A1109)","v":1100},null,null,null,null," =COUNTA(A10:A1109)"]
["No",null,{"$f":"\"Count of \"&E10","v":"Count of Yes"},{"$f":"COUNTIF($A$10:$A$1109,E10)","v":354},"Yes",null,null,null," =COUNTIF($A$10:$A$1109,F10)"]
["Yes",null,{"$f":"\"Count of \"&E11","v":"Count of No"},{"$f":"COUNTIF($A$10:$A$1109,E11)","v":746},"No",null,null,null," =COUNTIF($A$10:$A$1109,F11)"]
["No",null,{"$f":"\"P(\"&E10&\")\"","v":"P(Yes)"},{"$f":"D10/$D$9","v":0.32181818181818184},"sample proportion = Point Estimate","p","Proportion of potential employees who know Excel well",null," =D10/$D$9"]
["No",null,{"$f":"\"P(\"&E11&\")\"","v":"P(No)"},0.67818181818181822,null,null,null,null," =D11/$D$9"]
["Yes",null,"n*p>5",{"$f":"D9*D12","v":354},{"$f":"IF(D14=\"\",\"\",D14>5)","v":true},"Can we use Normal Curve?",null,null," =D9*D12"]
["No",null,"n*(1-p)>5",{"$f":"D9*D13","v":746},{"$f":"IF(D15=\"\",\"\",D15>5)","v":true},null,null,null," =D9*D13"]
["No",null,"Confidence Level",0.95,null,null,null,null," 0.95"]
["No",null,"Significance Level",{"$f":"1-D16","v":5.0000000000000044E-2},"alpha",null,null,null," =1-D16"]
["No",null,"alpha/2",{"$f":"D17/2","v":2.5000000000000022E-2},null,null,null,null," =D17/2"]
["Yes",null,"z upper",{"$f":"_xlfn.NORM.S.INV(1-D18)","v":1.9599639845400536},null,"Method 2",null,null," =NORM.S.INV(1-D18)"]
["Yes",null,"Standard Error",{"$f":"SQRT(D12*D13/D9)","v":1.4085816195069857E-2},"SQRT(p*(1-p)/n)",null,null,null," =SQRT(D12*D13/D9)"]
["No",null,"Margin of error",{"$f":"D20*D19","v":2.7607692435187934E-2},null,null,null,null," =D20*D19"]
["Yes",null,"Lower Limit",{"$f":"$D$12-$D$21","v":0.29421048938299388},null,null,null,null," =$D$12-$D$21"]
["No",null,"Upper Limit",{"$f":"$D$12+$D$21","v":0.34942587425336979},null,null,null,null," =$D$12+$D$21"]
["Yes",null,"Conclusion:"]
["No",null,{"$f":"IF(D23=\"\",\"\",\"The \"&TEXT(D16,\"0.00%\")&\" confidence interval for the \"&LOWER(G12)&\" is \"&TEXT(D22,\"0.0000\")&\" to \"&TEXT(D23,\"0.0000\")&\".\")","v":"The 95.00% confidence interval for the proportion of potential employees who know excel well is 0.2942 to 0.3494."}]
["Yes",null,"So, since this company hires people on the spot if they know their field and they know Excel, be sure to study both in school!"]
["No"]
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["Yes"]
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["Yes"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["Yes"]
["No"]
["Yes"]
["Yes"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["Yes"]
["No"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]
["Yes"]
["No"]
["No"]
["No"]
["No"]
["Yes"]

{"sheet":"Pbar(2)","index":11,"n_rows":24,"n_cols":5,"rows_kept":24,"cut":false,"hidden":false,"merged":[]}
["Furniture Land South surveyed their customers (n = 600) to see if they liked the new line of durable foam furniture decorated in bright colors. 414 said they were excited about the new line. All the binomial tests are met."]
[]
[1,"List Variables:"]
[null,"x = # of successes =",414]
[null,"n = sample size =",600]
[null,"Pbar = sample proportion = x/n =",null,null," =C4/C5"]
[]
[2,"What is the best estimation for the population proportion?"]
[null,{"$f":"IF(C6=\"\",\"\",\"Our sample proportion is the best estimate for the population proportion ==> p = \"&C6)","v":""}]
[]
[3,"Determine a 99% Confidence Interval: State the level of confidence, find z, and calculate the confidence intervals."]
[null,"Level of Confidence =",0.99]
[null,"Alpha = Risk that population proportion is not in our interval =",null,null," =1-C12"]
[null,"Alpha/2 =",null,null," =C13/2"]
[null,"z =",null,null," =NORM.S.INV(1-C14)"]
[null,"Standard Error",null,null," =SQRT(C6*(1-C6)/C5)"]
[null,"Margin of error",null,null," =C16*C15"]
[null,"Xbar lower end =",null,null," =C6-C17"]
[null,"Xbar upper end =",null,null," =C6+C17"]
[]
[4,"Conclusions"]
[null,{"$f":"IF(C19=\"\",\"\",\"The owner can be \"&TEXT(C12,\"0.00%\")&\" sure that the population proportion (% of customers excited about the new product) is between \"&TEXT(C18,\"0.00%\")&\" and \"&TEXT(C19,\"0.00%\")&\".\")","v":""}]
[null,{"$f":"IF(C19=\"\",\"\",\"The margin of error is \"&TEXT(C17,\"0.00%\")&\".\")","v":""}]
[null,{"$f":"IF(C19=\"\",\"\",\"If 100 similar intervals were constructed about \"&C12*100&\" intervals would contain the population proportion.\")","v":""}]

{"sheet":"Pbar(2an)","index":12,"n_rows":24,"n_cols":5,"rows_kept":24,"cut":false,"hidden":false,"merged":[]}
["Furniture Land South surveyed their customers (n = 600) to see if they liked the new line of durable foam furniture decorated in bright colors. 414 said they were excited about the new line. All the binomial tests are met."]
[]
[1,"List Variables:"]
[null,"x = # of successes =",414]
[null,"n = sample size =",600]
[null,"p = sample proportion = x/n =",{"$f":"C4/C5","v":0.69},null," =C4/C5"]
[]
[2,"What is the best estimation for the population proportion?"]
[null,{"$f":"\"Our sample proportion is the best estimate for the population proportion ==> p = \"&C6","v":"Our sample proportion is the best estimate for the population proportion ==> p = 0.69"}]
[]
[3,"Determine a 99% Confidence Interval: State the level of confidence, find z, and calculate the confidence intervals."]
[null,"Level of Confidence =",0.99]
[null,"Alpha = Risk that population proportion is not in our interval =",{"$f":"1-C12","v":1.0000000000000009E-2},null," =1-C12"]
[null,"Alpha/2 =",{"$f":"C13/2","v":5.0000000000000044E-3},null," =C13/2"]
[null,"z =",{"$f":"_xlfn.NORM.S.INV(1-C14)","v":2.5758293035488999},null," =NORMSINV(1-C14)"]
[null,"Standard Error",{"$f":"SQRT(C6*(1-C6)/C5)","v":1.8881207588499205E-2},null," =SQRT(C6*(1-C6)/C5)"]
[null,"Margin of error",{"$f":"C15*C16","v":4.8634767792846111E-2},null," =C16*C15"]
[null,"Xbar lower end =",{"$f":"$C$6-$C$17","v":0.6413652322071538},null," =C6-C17"]
[null,"Xbar upper end =",{"$f":"$C$6+$C$17","v":0.73863476779284609},null," =C6+C17"]
[]
[4,"Conclusions"]
[null,{"$f":"\"The owner can be \"&TEXT(C12,\"0.00%\")&\" sure that the population proportion (% of customers excited about the new product) is between \"&TEXT(C18,\"0.00%\")&\" and \"&TEXT(C19,\"0.00%\")&\".\"","v":"The owner can be 99.00% sure that the population proportion (% of customers excited about the new product) is between 64.14% and 73.86%."}]
[null,{"$f":"\"The margin of error is \"&TEXT(C17,\"0.00%\")&\".\"","v":"The margin of error is 4.86%."}]
[null,{"$f":"\"If 100 similar intervals were constructed about \"&C12*100&\" intervals would contain the population proportion.\"","v":"If 100 similar intervals were constructed about 99 intervals would contain the population proportion."}]

{"sheet":"Sample Size","index":13,"n_rows":27,"n_cols":3,"rows_kept":27,"cut":false,"hidden":false,"merged":[]}
["Error = ",5]
["Est. sigma",20]
["Level of confidence =",0.99]
["Alpha = Risk that pop. Mean, mu,  is not in our interval ="]
["Alpha/2 ="]
["z =",null," =NORM.S.INV(1-B5)"]
["Sample size estimate =",null," =(B6*B2/B1)^2"]
["sample size =",null," =ROUNDUP(B7,0)"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["ERROR =",0.03]
["p =",0.3]
["Level of confidence =",0.95]
["Alpha = Risk that population proportion is not in our interval ="]
["Alpha/2 ="]
["z =",null," =NORM.S.INV(1-B24)"]
["Sample size estimate =",null," =B21*(1-B21)*(B25/B20)^2"]
["sample size =",null," =ROUNDUP(B26,0)"]

{"sheet":"Sample Size(an)","index":14,"n_rows":27,"n_cols":3,"rows_kept":27,"cut":false,"hidden":false,"merged":[]}
["Error = ",5]
["Est. sigma",20]
["Level of confidence =",0.99]
["Alpha = Risk that pop. Mean, mu,  is not in our interval =",{"$f":"1-B3","v":1.0000000000000009E-2}]
["Alpha/2 =",{"$f":"B4/2","v":5.0000000000000044E-3}]
["z =",{"$f":"_xlfn.NORM.S.INV(1-B5)","v":2.5758293035488999}," =NORM.S.INV(1-B5)"]
["Sample size estimate =",{"$f":"(B6*B2/B1)^2","v":106.15834561633937}," =(B6*B2/B1)^2"]
["sample size =",{"$f":"ROUNDUP(B7,0)","v":107}," =ROUNDUP(B7,0)"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["ERROR =",0.03]
["p =",0.3]
["Level of confidence =",0.95]
["Alpha = Risk that population proportion is not in our interval =",{"$f":"1-B22","v":5.0000000000000044E-2}]
["Alpha/2 =",{"$f":"B23/2","v":2.5000000000000022E-2}]
["z =",{"$f":"_xlfn.NORM.S.INV(1-B24)","v":1.9599639845400536}," =NORM.S.INV(1-B24)"]
["Sample size estimate =",{"$f":"B21*(1-B21)*(B25/B20)^2","v":896.34039149529565}," =B21*(1-B21)*(B25/B20)^2"]
["sample size =",{"$f":"ROUNDUP(B26,0)","v":897}," =ROUNDUP(B26,0)"]