{"text_format":"1","workbook":"xlsx","n_sheets":14,"sheets":["Directions","1) Ttest1","2) F-Test","3) Probability Density","4) Expected Number per Bin","5) Histogram and Chi Square","6) Chi Square for Men","7) Generating Random Numbers","8) Drug Trial","9) Weight & CO","10) Multivariable Fit","11) Quiz","notes","Gaussians"],"not_rendered":{"charts":1,"images":7,"macros":1,"external_links":0,"defined_names":14,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Directions","index":0,"n_rows":4,"n_cols":1,"rows_kept":4,"cut":false,"hidden":false,"merged":[[5,0,5,12],[6,0,6,12],[7,0,7,12],[8,0,8,12],[15,0,15,12],[9,0,9,12],[10,0,10,12],[11,0,11,12],[12,0,12,12],[13,0,13,12],[0,0,0,12],[1,0,1,12],[2,0,2,12],[3,0,3,12],[4,0,4,12],[22,0,22,12],[14,0,14,12],[19,0,19,12],[20,0,20,12],[21,0,21,12],[16,0,16,12],[17,0,17,12],[18,0,18,12]]}
["Step through this file, from the tabs numbered 1) through 8) and perform the statistical analysis as described."]
["Turn in the answers to all of these exercises along with the answers to the quiz at the end."]
[]
["Where indicated place your answers in the yellow cells."]

{"sheet":"1) Ttest1","index":1,"n_rows":121,"n_cols":4,"rows_kept":121,"cut":false,"hidden":false,"merged":[[26,3,26,6],[27,3,27,6],[0,1,0,10],[1,1,1,10],[2,1,2,10],[5,1,5,10],[3,1,3,10],[4,1,4,10],[7,0,7,1]]}
["Problem 1","The data set below represents the heights of male and female students in inches.  Use a Student's T-test to determine"]
[null,"whether the difference in height between the two populations is statistically significant.  Because you"]
[null,"predicted that the height of female students would be less than the height of male students, you should use"]
[null,"a one-tailed test.  Assume that there the males and females are not paired through any considerations and that the"]
[null,"standard deviations of the two data sets are the same.  "]
[null,"Specifically answer the two questions highlighted in yellow in the space provided."]
[]
["Height (Inches)"]
["Women","Men"]
[63.001377755182126,62.785892330941152]
[63.021180347836072,64.091299555781617]
[64.199213223390402,65.609342774704658]
[67.324129379170728,63.582486735885837]
[64.618962727736204,71.159621959446724]
[63.231545485791067,66.433942023085194]
[67.389659556381233,66.441255395408561]
[62.405036275060212,61.021466196319444]
[65.110865768795179,64.109290361069284]
[63.605395523956332,69.977502851915062]
[59.048462743275188,67.155066993822203]
[60.454337077449303,66.533699837147878]
[60.893681849094975,63.675346710836962]
[66.292926634825562,66.152674239544623]
[62.953924531680471,63.137985954065101]
[64.741431046602301,70.154320196162942]
[68.401443470914273,68.281808751728235]
[64.571579189274374,64.321276285531326,null,"The p-value for this data set is"]
[62.073186416393128,66.525512925831052,null,"Is the difference in the means statistically significant?"]
[61.622124857198031,69.152988137455978]
[69.860737229270342,64.451239475334802]
[58.018659864318536,60.44698112399918]
[69.789838631632719,70.61514403800237]
[69.144604292716849,70.698159008089192]
[68.858343793053294,63.974635611674984]
[62.664704570975118,62.640730703657042]
[63.717685211999196,61.041017688894598]
[66.589237915465716,70.844686188446204]
[59.766504830244266,70.091644685890884]
[64.336832878224115,71.237128946454717]
[69.906193473502441,62.482316594128342]
[62.08771002682623,65.097221894837617]
[59.300330596569594,64.161556142829767]
[67.328182360971894,65.742454769678218]
[59.328706674806234,63.094050920684495]
[58.683180877853076,67.106248998497563]
[67.205652719941,60.554517347409096]
[66.626797829185193,62.095767017223693]
[63.571450987064104,69.873965439971272]
[69.647366789875292,63.713391880566363]
[66.901392602199067,67.558229228095882]
[65.333041860607679,64.913903424776151]
[69.37846827760967,69.259939028256028]
[59.205870159649194,60.442409592318171]
[67.816244076701139,68.805315112735855]
[64.685503972201019,66.758063771865778]
[60.084184931406178,60.897592329504555]
[65.174867027164865,71.327297386098394]
[60.715343078229623,63.683550478647298]
[58.474390680617439,61.317965360605569]
[64.869703507637169,61.968140831385597]
[67.72278174933075,61.861955757646705]
[60.628591939650043,65.013094683490095]
[60.971215999475881,66.122901122846287]
[63.056347422902711,67.99873986873402]
[69.127935594269047,63.185514917005008]
[68.064126393948854,69.666911638085494]
[59.777627385626296,60.47022981291893]
[60.460867648733696,69.847115771620523]
[61.738359152200864,60.715678028998958]
[64.102043877753772,63.454635505055464]
[67.442288891787229,60.230835324425257]
[61.346787523258357,68.350549950331242]
[66.293350276774717,67.255521626355574]
[62.081289568547191,70.524219832725549]
[65.416249622143027,64.530318472060813]
[58.942580755769981,64.809917332619008]
[61.488016304249456,70.76049651301156]
[60.309893618757904,62.122854881276922]
[67.760561341688998,65.892298673920152]
[66.777124067584907,67.265820683211189]
[67.615434436779921,71.661586656121756]
[68.783325295663261,60.73473923320006]
[63.451521718888763,63.964076209784729]
[62.670448769738115,61.789933297223712]
[69.54085648125475,64.179454436546536]
[68.648340886597225,67.847927785490242]
[62.401696204731891,68.229396957637121]
[66.625138974317011,63.053261505383446]
[69.388365702357561,70.843045179026589]
[65.401987722472185,61.527507705623123]
[67.153737385765496,64.788722697452641]
[61.711694632740496,67.2837518308216]
[66.587680176008817,62.92599244485038]
[64.164640951812487,67.580960816510981]
[60.264923308802445,63.55499262331832]
[64.084615640493155,70.582304563585495]
[68.128700908974508,65.291579327179548]
[62.370618784843963,67.964723273518246]
[63.474219721805667,69.95525924372545]
[58.344424759900313,67.648825581317794]
[60.196189557878959,71.126483096881117]
[62.764284967704981,61.01748982761989]
[67.802950270029001,67.02356162309286]
[63.425473395852734,61.959201163247599]
[61.74128444081618,62.605479585382987]
[66.112427975508837,68.140597244670502]
[60.361096344163272,61.561220869870581]
[59.156835146873291,65.417296730142937]
[58.331054765299896,66.630508727787557]
[69.439813656941993,69.37764827720045]
[66.667565708183915,60.510809080245551]
[58.205339804973988,66.466452363910975]
[65.61694334440611,63.654087893532108]
[61.096669691609264,68.904469681615566]
[68.145859086729544,67.541546974895795]
[60.97639296656363,61.158511522865126]
[58.606224622175937,67.239462278478214]
[61.63839568145071,69.455571491101793]
[64.029397558956461,70.227758696531694]
[{"$f":"AVERAGE(A10:A119)","v":64.024243692482244},{"$f":"AVERAGE(B10:B119)","v":65.715489583008861},"Means"]
[{"$f":"STDEV(A10:A119)","v":3.4271936433784589},{"$f":"STDEV(B10:B119)","v":3.3391107883203208},"St Devs"]

{"sheet":"2) F-Test","index":2,"n_rows":118,"n_cols":3,"rows_kept":118,"cut":false,"hidden":false,"merged":[[26,2,26,6],[27,2,27,6],[0,1,0,10],[1,1,1,10],[2,1,2,10],[3,1,3,10],[4,0,4,1]]}
["Problem 2","Now use an F-test on the same data set to decide whether the standard deviations of the two data sets are equal."]
[null,"Specifically answer the two questions highlighted in yellow in the space provided."]
[]
[]
["Height (Inches)"]
["Women","Men"]
[63.001377755182126,62.785892330941152]
[63.021180347836072,64.091299555781617]
[64.199213223390402,65.609342774704658]
[67.324129379170728,63.582486735885837]
[64.618962727736204,71.159621959446724]
[63.231545485791067,66.433942023085194]
[67.389659556381233,66.441255395408561]
[62.405036275060212,61.021466196319444]
[65.110865768795179,64.109290361069284]
[63.605395523956332,69.977502851915062]
[59.048462743275188,67.155066993822203]
[60.454337077449303,66.533699837147878]
[60.893681849094975,63.675346710836962]
[66.292926634825562,66.152674239544623]
[62.953924531680471,63.137985954065101]
[64.741431046602301,70.154320196162942]
[68.401443470914273,68.281808751728235]
[64.571579189274374,64.321276285531326]
[62.073186416393128,66.525512925831052]
[61.622124857198031,69.152988137455978]
[69.860737229270342,64.451239475334802,"The p-value for this data set is:"]
[58.018659864318536,60.44698112399918,"Is the difference in the standard deviations statistically significant?"]
[69.789838631632719,70.61514403800237]
[69.144604292716849,70.698159008089192]
[68.858343793053294,63.974635611674984]
[62.664704570975118,62.640730703657042]
[63.717685211999196,61.041017688894598]
[66.589237915465716,70.844686188446204]
[59.766504830244266,70.091644685890884]
[64.336832878224115,71.237128946454717]
[69.906193473502441,62.482316594128342]
[62.08771002682623,65.097221894837617]
[59.300330596569594,64.161556142829767]
[67.328182360971894,65.742454769678218]
[59.328706674806234,63.094050920684495]
[58.683180877853076,67.106248998497563]
[67.205652719941,60.554517347409096]
[66.626797829185193,62.095767017223693]
[63.571450987064104,69.873965439971272]
[69.647366789875292,63.713391880566363]
[66.901392602199067,67.558229228095882]
[65.333041860607679,64.913903424776151]
[69.37846827760967,69.259939028256028]
[59.205870159649194,60.442409592318171]
[67.816244076701139,68.805315112735855]
[64.685503972201019,66.758063771865778]
[60.084184931406178,60.897592329504555]
[65.174867027164865,71.327297386098394]
[60.715343078229623,63.683550478647298]
[58.474390680617439,61.317965360605569]
[64.869703507637169,61.968140831385597]
[67.72278174933075,61.861955757646705]
[60.628591939650043,65.013094683490095]
[60.971215999475881,66.122901122846287]
[63.056347422902711,67.99873986873402]
[69.127935594269047,63.185514917005008]
[68.064126393948854,69.666911638085494]
[59.777627385626296,60.47022981291893]
[60.460867648733696,69.847115771620523]
[61.738359152200864,60.715678028998958]
[64.102043877753772,63.454635505055464]
[67.442288891787229,60.230835324425257]
[61.346787523258357,68.350549950331242]
[66.293350276774717,67.255521626355574]
[62.081289568547191,70.524219832725549]
[65.416249622143027,64.530318472060813]
[58.942580755769981,64.809917332619008]
[61.488016304249456,70.76049651301156]
[60.309893618757904,62.122854881276922]
[67.760561341688998,65.892298673920152]
[66.777124067584907,67.265820683211189]
[67.615434436779921,71.661586656121756]
[68.783325295663261,60.73473923320006]
[63.451521718888763,63.964076209784729]
[62.670448769738115,61.789933297223712]
[69.54085648125475,64.179454436546536]
[68.648340886597225,67.847927785490242]
[62.401696204731891,68.229396957637121]
[66.625138974317011,63.053261505383446]
[69.388365702357561,70.843045179026589]
[65.401987722472185,61.527507705623123]
[67.153737385765496,64.788722697452641]
[61.711694632740496,67.2837518308216]
[66.587680176008817,62.92599244485038]
[64.164640951812487,67.580960816510981]
[60.264923308802445,63.55499262331832]
[64.084615640493155,70.582304563585495]
[68.128700908974508,65.291579327179548]
[62.370618784843963,67.964723273518246]
[63.474219721805667,69.95525924372545]
[58.344424759900313,67.648825581317794]
[60.196189557878959,71.126483096881117]
[62.764284967704981,61.01748982761989]
[67.802950270029001,67.02356162309286]
[63.425473395852734,61.959201163247599]
[61.74128444081618,62.605479585382987]
[66.112427975508837,68.140597244670502]
[60.361096344163272,61.561220869870581]
[59.156835146873291,65.417296730142937]
[58.331054765299896,66.630508727787557]
[69.439813656941993,69.37764827720045]
[66.667565708183915,60.510809080245551]
[58.205339804973988,66.466452363910975]
[65.61694334440611,63.654087893532108]
[61.096669691609264,68.904469681615566]
[68.145859086729544,67.541546974895795]
[60.97639296656363,61.158511522865126]
[58.606224622175937,67.239462278478214]
[61.63839568145071,69.455571491101793]
[64.029397558956461,70.227758696531694]
[{"$f":"AVERAGE(A7:A116)","v":64.024243692482244},{"$f":"AVERAGE(B7:B116)","v":65.715489583008861},"Means"]
[{"$f":"STDEV(A7:A116)","v":3.4271936433784589},{"$f":"STDEV(B7:B116)","v":3.3391107883203208},"St. Devs."]

{"sheet":"3) Probability Density","index":3,"n_rows":60,"n_cols":9,"rows_kept":60,"cut":false,"hidden":false,"merged":[[12,2,12,8],[13,2,13,8],[14,2,14,8],[15,2,15,8],[0,2,0,8],[1,2,1,8],[2,2,2,8],[3,2,3,8],[8,2,8,8],[11,2,11,8],[4,2,4,8],[5,2,5,8],[6,2,6,8],[7,2,7,8],[9,2,9,8],[10,2,10,8]]}
[null,"Problem 3","The T-test used in problem 1 assumed that the distribution of the data was Gaussian.  To explore this assumption,"]
[null,null,"first generate a Gaussian curve based on the mean and standard deviation of the data.  You will need values"]
[null,null,"for the mean and standard deviation (for women), which you can calculate from the data on the Ttest tab (they are"]
[null,null,"also given in cells H21 and H22, respectively, of this spreadsheet)."]
[]
[null,null,"Specific Instructions:"]
[null,null,"1. In Column C, starting at Line 19, calculate f(x) directly from the x-values in Column B."]
[null,null,"2. In Column D, starting at Line 19, calculate f(x) with the Excel function NORMDIST(x, mean, stdev, cumulative)."]
[null,null,"3. In Column E, starting at Line 19, calculate F(x) with the Excel function NORMDIST(x, mean, stdev, cumulative)"]
[null,null,"   (Notice that the value of cumulative will be 0 for Task 2 and 1 for Task 3.)"]
[null,null,"4. In Column E, starting at Line 19, claculate F(x) with the Excel function erf(a,b)."]
[null,null,"   (Hint: You will need to combine Eq. A1 and A4 from the tutorial.)"]
[null,null,"5. Plot, on the same graph, the probability density functions generated in Tasks 1 and 2."]
[null,null,"6. Plot on the same graph, the cumulative probability distributions generated in Tasks 3 and 4."]
[]
[]
[]
[null,"x","f(x) (Equation)","f(x) (NORMDIST)","F(x) (NORMDIST)","F(x) (ERF(x))"]
[null,55]
[null,55.5]
[null,56,null,null,null,null,null,"xmean=",64.024243692482202]
[null,56.5,null,null,null,null,null,"sigma=",3.4271936433784589]
[null,57]
[null,57.5]
[null,58]
[null,58.5]
[null,59]
[null,59.5]
[null,60]
[null,60.5]
[null,61]
[null,61.5]
[null,62]
[null,62.5]
[null,63]
[null,63.5]
[null,64]
[null,64.5]
[null,65]
[null,65.5]
[null,66]
[null,66.5]
[null,67]
[null,67.5]
[null,68]
[null,68.5]
[null,69]
[null,69.5]
[null,70]
[null,70.5]
[null,71]
[null,71.5]
[null,72]
[null,72.5]
[null,73]
[null,73.5]
[null,74]
[null,74.5]
[null,75]
[null,"Integral=",{"$f":"SUM(C19:C59)*0.5","v":0}]

{"sheet":"4) Expected Number per Bin","index":4,"n_rows":58,"n_cols":7,"rows_kept":58,"cut":false,"hidden":false,"merged":[[5,2,5,8],[0,2,0,8],[1,2,1,8],[2,2,2,8],[3,2,3,8],[4,2,4,8],[12,2,12,8],[13,2,13,8],[14,2,14,8],[6,2,6,8],[7,2,7,8],[8,2,8,8],[9,2,9,8],[10,2,10,8],[11,2,11,8]]}
[null,"Problem 4","If you have performed the third task of spreadsheet 3 correctly, the cumulative probability distribution for the"]
[null,null,"Gaussian function will appear on this spreadsheet, beginning at line 15.  Use these values to determine a set of"]
[null,null,"bins that should have roughly the same number of data values, assuming that the data follow the given gaussian"]
[null,null,"distribution."]
[]
[null,null,"Tasks:"]
[null,null,"1) In Column D, beginning at Line 18, calculate the number of expected data values that should be less than the"]
[null,null,"    value of x on the corresponding line of Column B.  (For example, since there are 110 points, you know that all 110"]
[null,null,"    points must have a value that is less than infinity, and 55 points should have values that are less than xmean)."]
[null,null,"    The task reduces to simply multiplying the value in Column C by 110."]
[null,null,"2) Find the values of x that would give roughly 10 data values in each bin.  For example, start with x1 = 59.5 so that the bin"]
[null,null,"    from -infinity to x1 will have roughly 10 values.  Then take x2 = 61 because 20.765 - 10.27 is roughly 10."]
[null,null,"    Put the appropriate x values in Column F (starting with Row 18) and put the expected number of points in"]
[null,null,"    Column G.  You will have 5 values of x in Column F.  At the end of the N values in Column G, add an extra"]
[null,null,"    value that represents the number of data points that are expected to be larger than the last x value."]
[]
[null,"x","F(x) (NORMDIST())","N < x",null,"x","N"]
[null,55,{"$f":"'3) Probability Density'!E19","v":0}]
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[null,56,{"$f":"'3) Probability Density'!E21","v":0}]
[null,56.5,{"$f":"'3) Probability Density'!E22","v":0}]
[null,57,{"$f":"'3) Probability Density'!E23","v":0}]
[null,57.5,{"$f":"'3) Probability Density'!E24","v":0}]
[null,58,{"$f":"'3) Probability Density'!E25","v":0}]
[null,58.5,{"$f":"'3) Probability Density'!E26","v":0}]
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[null,59.5,{"$f":"'3) Probability Density'!E28","v":0}]
[null,60,{"$f":"'3) Probability Density'!E29","v":0}]
[null,60.5,{"$f":"'3) Probability Density'!E30","v":0}]
[null,61,{"$f":"'3) Probability Density'!E31","v":0}]
[null,61.5,{"$f":"'3) Probability Density'!E32","v":0}]
[null,62,{"$f":"'3) Probability Density'!E33","v":0}]
[null,62.5,{"$f":"'3) Probability Density'!E34","v":0}]
[null,63,{"$f":"'3) Probability Density'!E35","v":0}]
[null,63.5,{"$f":"'3) Probability Density'!E36","v":0}]
[null,64,{"$f":"'3) Probability Density'!E37","v":0}]
[null,64.5,{"$f":"'3) Probability Density'!E38","v":0}]
[null,65,{"$f":"'3) Probability Density'!E39","v":0}]
[null,65.5,{"$f":"'3) Probability Density'!E40","v":0}]
[null,66,{"$f":"'3) Probability Density'!E41","v":0}]
[null,66.5,{"$f":"'3) Probability Density'!E42","v":0}]
[null,67,{"$f":"'3) Probability Density'!E43","v":0}]
[null,67.5,{"$f":"'3) Probability Density'!E44","v":0}]
[null,68,{"$f":"'3) Probability Density'!E45","v":0}]
[null,68.5,{"$f":"'3) Probability Density'!E46","v":0}]
[null,69,{"$f":"'3) Probability Density'!E47","v":0}]
[null,69.5,{"$f":"'3) Probability Density'!E48","v":0}]
[null,70,{"$f":"'3) Probability Density'!E49","v":0}]
[null,70.5,{"$f":"'3) Probability Density'!E50","v":0}]
[null,71,{"$f":"'3) Probability Density'!E51","v":0}]
[null,71.5,{"$f":"'3) Probability Density'!E52","v":0}]
[null,72,{"$f":"'3) Probability Density'!E53","v":0}]
[null,72.5,{"$f":"'3) Probability Density'!E54","v":0}]
[null,73,{"$f":"'3) Probability Density'!E55","v":0}]
[null,73.5,{"$f":"'3) Probability Density'!E56","v":0}]
[null,74,{"$f":"'3) Probability Density'!E57","v":0}]
[null,74.5,{"$f":"'3) Probability Density'!E58","v":0}]
[null,75,{"$f":"'3) Probability Density'!E59","v":0}]

{"sheet":"5) Histogram and Chi Square","index":5,"n_rows":129,"n_cols":15,"rows_kept":129,"cut":false,"hidden":false,"merged":[[4,1,4,13],[5,1,5,13],[6,1,6,13],[0,1,0,13],[1,1,1,13],[2,1,2,13],[3,1,3,13]]}
["Problem 5","1) A set of bin values is shown in Column F, starting at Row 18.  (These values are different from those that you were asked to provide in Problem 4.)  Use these values"]
[null,"    and the Histogram option under \"Data Analysis\" to generate a histogram of the height data in Column A."]
[null,"2) Create a column plot that compares the expected number of points in each bin to the number of points from the histogram."]
[null,"3) For each bin, calculate the value of (O-E)2/E, where O is the observed number of data values in each bin and E is the expected number of values in each bin."]
[null,"4) Given that the degrees of freedom is the number of bins minus 3 in this case, calculate the p value from the chi squared statistic.(Use CHIDIST())."]
[null,"5) At the p = 0.05 level, does the test suggest that the probability distribution is significantly different from a normal distribition?"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Height (in.)"]
["Women",null,null,null,null,"Bins","Expected N","Histogram","(O-E)2/E",null,null,null,null,"Bin","Frequency"]
[63.001377755182126,null,null,null,null,60.5,16.709023876489052,null,null,null,"xmean=",64.024243692482202]
[63.021180347836072,null,null,null,null,62,13.802802344641549,null,null,null,"sigma=",3.4271936433784589]
[64.199213223390402,null,null,null,null,63.5,17.801558799472712]
[67.324129379170728,null,null,null,null,65,19.013966965905304]
[64.618962727736204,null,null,null,null,66.5,16.819498516891699]
[63.231545485791067,null,null,null,null,69,17.793201038418019]
[67.389659556381233,null,null,null,null,"more",8.0599484581816654]
[62.405036275060212,null,null,null,null,null,null,"Sum(O-E)2=",{"$f":"SUM(I18:I24)","v":0}]
[65.110865768795179]
[63.605395523956332,null,null,null,null,null,null,"p=",{"$f":"CHIDIST(I25,7-3)","v":1}]
[59.048462743275188]
[60.454337077449303]
[60.893681849094975]
[66.292926634825562]
[62.953924531680471]
[64.741431046602301]
[68.401443470914273]
[64.571579189274374]
[62.073186416393128]
[61.622124857198031]
[69.860737229270342]
[58.018659864318536]
[69.789838631632719]
[69.144604292716849]
[68.858343793053294]
[62.664704570975118]
[63.717685211999196]
[66.589237915465716]
[59.766504830244266]
[64.336832878224115]
[69.906193473502441]
[62.08771002682623]
[59.300330596569594]
[67.328182360971894]
[59.328706674806234]
[58.683180877853076]
[67.205652719941]
[66.626797829185193]
[63.571450987064104]
[69.647366789875292]
[66.901392602199067]
[65.333041860607679]
[69.37846827760967]
[59.205870159649194]
[67.816244076701139]
[64.685503972201019]
[60.084184931406178]
[65.174867027164865]
[60.715343078229623]
[58.474390680617439]
[64.869703507637169]
[67.72278174933075]
[60.628591939650043]
[60.971215999475881]
[63.056347422902711]
[69.127935594269047]
[68.064126393948854]
[59.777627385626296]
[60.460867648733696]
[61.738359152200864]
[64.102043877753772]
[67.442288891787229]
[61.346787523258357]
[66.293350276774717]
[62.081289568547191]
[65.416249622143027]
[58.942580755769981]
[61.488016304249456]
[60.309893618757904]
[67.760561341688998]
[66.777124067584907]
[67.615434436779921]
[68.783325295663261]
[63.451521718888763]
[62.670448769738115]
[69.54085648125475]
[68.648340886597225]
[62.401696204731891]
[66.625138974317011]
[69.388365702357561]
[65.401987722472185]
[67.153737385765496]
[61.711694632740496]
[66.587680176008817]
[64.164640951812487]
[60.264923308802445]
[64.084615640493155]
[68.128700908974508]
[62.370618784843963]
[63.474219721805667]
[58.344424759900313]
[60.196189557878959]
[62.764284967704981]
[67.802950270029001]
[63.425473395852734]
[61.74128444081618]
[66.112427975508837]
[60.361096344163272]
[59.156835146873291]
[58.331054765299896]
[69.439813656941993]
[66.667565708183915]
[58.205339804973988]
[65.61694334440611]
[61.096669691609264]
[68.145859086729544]
[60.97639296656363]
[58.606224622175937]
[61.63839568145071]
[64.029397558956461]
[{"$f":"AVERAGE(A18:A127)","v":64.024243692482244}]
[{"$f":"STDEV(A18:A127)","v":3.4271936433784589}]

{"sheet":"6) Chi Square for Men","index":6,"n_rows":119,"n_cols":3,"rows_kept":119,"cut":false,"hidden":false,"merged":[[0,2,0,11],[1,2,1,11],[2,2,2,11],[3,2,3,11]]}
[null,"Problem 6","Repeat the analysis of Problems 4 and 5 for the data collected on Men"]
[]
[]
[]
[]
[]
["Men"]
[62.785892330941152]
[64.091299555781617]
[65.609342774704658]
[63.582486735885837]
[71.159621959446724]
[66.433942023085194]
[66.441255395408561]
[61.021466196319444]
[64.109290361069284]
[69.977502851915062]
[67.155066993822203]
[66.533699837147878]
[63.675346710836962]
[66.152674239544623]
[63.137985954065101]
[70.154320196162942]
[68.281808751728235]
[64.321276285531326]
[66.525512925831052]
[69.152988137455978]
[64.451239475334802]
[60.44698112399918]
[70.61514403800237]
[70.698159008089192]
[63.974635611674984]
[62.640730703657042]
[61.041017688894598]
[70.844686188446204]
[70.091644685890884]
[71.237128946454717]
[62.482316594128342]
[65.097221894837617]
[64.161556142829767]
[65.742454769678218]
[63.094050920684495]
[67.106248998497563]
[60.554517347409096]
[62.095767017223693]
[69.873965439971272]
[63.713391880566363]
[67.558229228095882]
[64.913903424776151]
[69.259939028256028]
[60.442409592318171]
[68.805315112735855]
[66.758063771865778]
[60.897592329504555]
[71.327297386098394]
[63.683550478647298]
[61.317965360605569]
[61.968140831385597]
[61.861955757646705]
[65.013094683490095]
[66.122901122846287]
[67.99873986873402]
[63.185514917005008]
[69.666911638085494]
[60.47022981291893]
[69.847115771620523]
[60.715678028998958]
[63.454635505055464]
[60.230835324425257]
[68.350549950331242]
[67.255521626355574]
[70.524219832725549]
[64.530318472060813]
[64.809917332619008]
[70.76049651301156]
[62.122854881276922]
[65.892298673920152]
[67.265820683211189]
[71.661586656121756]
[60.73473923320006]
[63.964076209784729]
[61.789933297223712]
[64.179454436546536]
[67.847927785490242]
[68.229396957637121]
[63.053261505383446]
[70.843045179026589]
[61.527507705623123]
[64.788722697452641]
[67.2837518308216]
[62.92599244485038]
[67.580960816510981]
[63.55499262331832]
[70.582304563585495]
[65.291579327179548]
[67.964723273518246]
[69.95525924372545]
[67.648825581317794]
[71.126483096881117]
[61.01748982761989]
[67.02356162309286]
[61.959201163247599]
[62.605479585382987]
[68.140597244670502]
[61.561220869870581]
[65.417296730142937]
[66.630508727787557]
[69.37764827720045]
[60.510809080245551]
[66.466452363910975]
[63.654087893532108]
[68.904469681615566]
[67.541546974895795]
[61.158511522865126]
[67.239462278478214]
[69.455571491101793]
[70.227758696531694]
[{"$f":"AVERAGE(A8:A117)","v":65.715489583008861}]
[{"$f":"STDEV(A8:A117)","v":3.3391107883203208}]

{"sheet":"7) Generating Random Numbers","index":7,"n_rows":54,"n_cols":4,"rows_kept":54,"cut":false,"hidden":false,"merged":[[5,1,5,15],[6,1,6,15],[7,1,7,15],[8,1,8,15],[9,1,9,15],[0,1,0,15],[1,1,1,15],[2,1,2,15],[3,1,3,15],[4,1,4,15]]}
["Problem 7","1) In Column A, beginning with the first number on Line 13, generate a sequence of 40 Normally distributed random numbers with a mean of 50 and a standard deviation of 5."]
[null,"2) In Column B, beginning on Line 13, generate a sequence of 40 uniformly distributed random numbers with a mean of 50 and a standard deviation of 5."]
[null,"3) At the bottom of each column, calculate the mean and standard deviation of the corresponding set of numbers and verify that they are approximately 50 and 5, respectively"]
[null,"    for both sets of random numbers."]
[null,"4) Copy the two columns of random numbers onto columns C and D.  Use the \"Paste Values\" option to ensure that the numbers do not change.  Then sort Column C and Colum D"]
[null,"    from the lowest value to the highest value.  Now plot the random numbers.  (The x-axis will be the number's position, where the smallest number in each column has an x"]
[null,"    value of 1 and the largest value in each column has an x value of 40)."]
[null,"5) Is it possible to identify a qualitative difference between the two curves that have been generated?"]
[]
[]
[null,null,"Sorted","Sorted"]
["Normal","Uniform","Normal","Uniform"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[{"$f":"AVERAGE(A13:A52)","v":{"$error":"#DIV/0!"}},{"$f":"AVERAGE(B13:B52)","v":{"$error":"#DIV/0!"}}]
[{"$f":"STDEV(A13:A52)","v":{"$error":"#DIV/0!"}},{"$f":"STDEV(B13:B52)","v":{"$error":"#DIV/0!"}}]

{"sheet":"8) Drug Trial","index":8,"n_rows":61,"n_cols":6,"rows_kept":61,"cut":false,"hidden":false,"merged":[[9,5,9,11],[2,4,2,14],[4,4,4,14],[5,4,5,14],[6,4,6,14],[0,0,0,1],[0,4,0,14],[3,4,3,14],[1,4,1,14],[8,5,8,11]]}
["Problem 8: ",null,null,null,"The two data sets below are from clinical trials comparing Brand X and Brand Y as blood pressure reducing drugs."]
[null,null,null,null,"Each set is systolic pressure in mm Hg.  One group of subjects was given Brand X and the other was given Brand Y."]
[null,null,null,null,"Thus, it is not reasonable to use a paired T-test."]
[null,null,null,null,"1) Use an F-test to determine whether the standard deviations of the data can be considered to be the same."]
[null,null,null,null,"2) Use a Students T-Test (two-tailed) to determine whether the mean for Brand X is statistically different from the mean"]
[null,null,null,null,"    for Brand Y."]
[]
[]
["Brand X","Brand Y",null,null,null,"The p value for the F-test is:"]
[155.12806616103174,138.56178373246578,null,null,null,"The p value for the two-tailed student's t-test is:"]
[149.75360649426671,149.01525726117006]
[152.86210604491126,192.06312566124333]
[153.63458789904274,134.2267558815476]
[131.75087882517465,122.59660436164488]
[163.38319325823238,150.2744598447355]
[131.82368106573628,127.9254127232546]
[106.7336138417687,178.10563887185947]
[150.13072165183331,133.38229665994655]
[122.89039204929492,126.42043312915706]
[179.87761288309125,113.99592280829717]
[145.13023935883297,157.603309402338]
[132.85976688917282,54.638083959844408]
[155.73473951746575,100.23108693784037]
[151.71763230579225,99.72971347142996]
[126.06787821697407,129.11267344803883]
[109.02926665499808,122.55371993523136]
[134.65793627640392,109.70270681680192]
[91.568490072365336,100.63220242364427]
[156.34599247551415,155.73499715127505]
[123.16873349034441,123.07165261292531]
[171.10025508927609,150.39260284554081]
[136.34521481415752,107.28140716475049]
[137.05487525140637,167.81785341722667]
[110.12660255466265,124.62902669169254]
[99.711456409688168,125.17591594294156]
[168.91587952255867,110.23255838880111]
[207.23702831713001,167.36829065412093]
[147.31887491924562,121.30568715531615]
[144.15684986080811,104.69646486794332]
[144.18984077962548,113.48353307171425]
[154.37588344472175,137.28220126033168]
[146.18806500892447,111.69222488181393]
[84.839411098358823,106.49976710746746]
[119.63798043020623,169.8404912146957]
[114.08578168677383,82.890971063818995]
[172.18304127780735,133.68104436381194]
[144.89112213781812,178.20696343779997]
[158.34681094017827,168.30842194612814]
[160.01243475282251,145.53808915496793]
[138.78690057667592,192.55784113214366]
[151.35002903252982,100.45975256733368]
[192.84513048747721,116.82595934909115]
[68.855814207353703,158.90996072000999]
[171.88613613191208,130.40742761782275]
[147.92517959536465,152.15290170872444]
[171.32528625701525,70.329791440454869]
[192.8257299882458,90.404180680136704]
[73.548660323297227,92.293578732592891]
[178.28801320342683,95.260664452892428]
[{"$f":"AVERAGE(A10:A59)","v":142.65206847063436},{"$f":"AVERAGE(B10:B59)","v":128.91006820253551}]
[{"$f":"SQRT(VAR(A10:A59))","v":29.442427624565141},{"$f":"SQRT(VAR(B10:B59))","v":30.513143466597491}]

{"sheet":"9) Weight & CO","index":9,"n_rows":31,"n_cols":5,"rows_kept":31,"cut":false,"hidden":false,"merged":[[30,4,30,9],[30,10,30,11],[0,0,0,1],[0,2,0,12],[1,2,1,12],[2,2,2,12]]}
["Problem 9: ",null,"You propose that cardiac output increases with body weight.  Perform a least squares fit on the data below and"]
[null,null,"use the p-statistic to determine whether your hypothesis is correct."]
[]
[]
[]
[null,null,"Body Weight","Cariac Output"]
[null,null,195.21344360171958,6.9226498735406583]
[null,null,186.25601082377787,6.9665462767141166]
[null,null,191.43684340818541,6.5776235312530797]
[null,null,192.72431316507124,4.69351851033068]
[null,null,156.25146470862441,5.0657699454813923]
[null,null,208.97198876372062,4.7808629461243504]
[null,null,156.37280177622711,5.2475223511668752]
[null,null,114.5560230696145,5.498426080095542]
[null,null,186.88453608638883,6.466817448935438]
[null,null,141.48398674882486,6.6911366537652803]
[null,null,236.46268813848542,7.506262156985076]
[null,null,178.55039893138829,6.9908238770784683]
[null,null,158.09961148195472,2.8633229223812737]
[null,null,196.22456586244292,5.6793381372510705]
[null,null,189.52938717632043,5.4349896130425597]
[null,null,146.77979702829012,4.9609355472298251]
[null,null,118.38211109166346,4.7767824416242703]
[null,null,161.09656046067317,4.8007066162229517]
[null,null,89.280816787275555,4.05662118488884]
[null,null,197.2433207925236,7.5641061453216363]
[null,null,141.94788915057401,4.5952833182170263]
[null,null,221.8337584821268,6.22210121657701]
[]
[]
[null,null,null,null,"The p statistic for this data set is:"]

{"sheet":"10) Multivariable Fit","index":10,"n_rows":2,"n_cols":2,"rows_kept":2,"cut":false,"hidden":false,"merged":[[1,1,1,4]]}
[]
[null,"This exercise has not yet been written."]

{"sheet":"11) Quiz","index":11,"n_rows":18,"n_cols":14,"rows_kept":18,"cut":false,"hidden":false,"merged":[[0,0,0,12],[5,1,5,12],[6,1,6,12],[7,1,7,12],[2,1,2,12],[3,1,3,12],[4,1,4,12],[21,1,21,12],[22,1,22,12],[13,1,13,12],[16,1,16,12],[17,1,17,12],[18,1,18,12],[14,1,14,12],[8,0,8,12],[15,0,15,12],[19,1,19,12],[20,1,20,12],[9,1,9,12],[10,1,10,12],[11,1,11,12],[12,1,12,12]]}
["For each condition below, state which statistical test you should use. (F-test, T-test, Chi square, Pearson's)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Answer"]
["1)","You wish to compare the means of two data sets."]
["2) ","You wish to compare the standard deviations of two data sets."]
["3) ","You wish to compare the distribution of a data set to a hypothesized distribution."]
["4)","You wish to determine whether one variable depends on another variable."]
[]
[]
["State which type of T-test you should use in the following situations. (paired/unpaired, 1 tailed/2 tailed)"]
[]
["1)","You have data for heart rate for before and after exercise for 15 people and you propose that exercise increases heart rate."]
["2)","You have data for heart rate after exercise for men and women and you propose that the post-exercise heart rate will be higher"]
[null,"for women."]
["3)","You have data for heart rate for before and after exercise for 15 people and you propose that exercise changes heart rate."]
[]
["What statistical test would you use for the following situation?"]
["1)","You have data for heart rate after exercise for 20 different exercise durations and you propose that the heart rate will correlate"]
[null,"with the duration of the exercise."]

{"sheet":"notes","index":12,"n_rows":38,"n_cols":9,"rows_kept":38,"cut":false,"hidden":false,"merged":[[1,0,1,7],[1,8,1,13],[4,0,4,7]]}
[]
["For problem 1, the original distributions are uniform with means of 62 and 66 inches",null,null,null,null,null,null,null,"max and min are +/-4 from mean."]
[null,null,{"$f":"62+(RAND()-0.5)*8","v":63.617994145977853},{"$f":"66+(RAND()-0.5)*8","v":67.750010876356981}]
[]
["answer: p = 0.0001554 indicates that the difference in means is singificant."]
[]
[]
[]
[]
[]
[null,null,"Bin (Normalized)","Bin (Non-Normalized)","O","E","(O-E)2/E"]
[null,null,-1.2,4.6756231828060617,6,5.7534867179999996,1.0562081948028884E-2]
[null,null,-0.7,4.831203116195673,8,6.3446959319999996,0.43186176089507677]
[null,null,-0.4,4.9245510762294398,6,5.130730271,0.1472753042635504]
[null,null,0,5.0490150229411288,8,7.771087079,6.7430881764736772E-3]
[null,null,0.4,5.1734789696528178,3,7.771087079,2.9292262052904414]
[null,null,0.7,5.2668269296865846,7,5.130730271,0.68102767738649916]
[null,null,1.2,5.4224068630761959,5,6.3446959319999996,0.28499508391213912]
[null,null,10,8.1606136907333582,7,5.7534867179999996,0.27006151892926167]
[null,null,null,"More",0,null,4.7617527208014705,"=chi^2"]
[]
[]
[]
[null,null,"Lower critical values of chi-square distribution with  degrees of"]
[null,null,"  freedom "]
[]
[]
[null,null,"               Probability of exceeding the critical value"]
[null,null,"               0.90     0.95     0.975      0.99     0.999"]
[]
[]
[]
[null,null,"    1.          .016      .004      .001      .000      .000"]
[null,null,"    2.          .211      .103      .051      .020      .002"]
[null,null,"    3.          .584      .352      .216      .115      .024"]
[null,null,"    4.         1.064      .711      .484      .297      .091"]
[null,null,"    5.         1.610     1.145      .831      .554      .210"]
[null,null,"    6.         2.204     1.635     1.237      .872      .381"]

{"sheet":"Gaussians","index":13,"n_rows":58,"n_cols":6,"rows_kept":58,"cut":false,"hidden":false,"merged":[[0,0,0,1],[0,2,0,12],[1,2,1,12],[2,2,2,12]]}
["Problem 6: "]
[]
[]
[]
[]
[null,null,null,null,"Brand X","Brand Y"]
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