{"text_format":"3","workbook":"xlsx","n_sheets":4,"sheets":["SampMeans","Sheet2","Sheet3","Sheet4"],"not_rendered":{"charts":3,"macros":1,"defined_names":20,"comments":1},"read":"whole","date_system":"1900"}

{"sheet":"SampMeans","index":0,"n_rows":62,"n_cols":15,"rows_kept":62}
[null,"         Simulating the Distribution of the "]
[null,null,"       Difference of Sample Means"]
[]
[null,null,"This DIGMath module simulates the distribution "]
[null,null,"          of the differences of  sample means "]
[null,null,"         based on repeated random samples"]
[null,null,"   drawn from a variety of population patterns."]
[]
["What is the first population?",null,null,{"$f":"IF(E9=TRUE, 1,IF(E10=TRUE, 2,IF(E12=TRUE,3,4)))","v":4},"Normal population",null,2]
[{"$nulls":4},"Uniform population"]
[{"$nulls":4},"U-shaped population"]
[{"$nulls":4},"Skewed population"]
[]
[]
["What is the sample size n (2-50)?",null,null,{"$f":"E15","v":17},17]
[]
["The mean and standard deviation ",{"$nulls":3},"          m =     ",{"$f":"IF(pop=1,Sheet2!B2,IF(pop=2,Sheet2!E2,IF(pop=3,Sheet2!G2,Sheet2!I2)))","v":68.47}]
[null,"of this population are:",null,null,"      s =",{"$f":"IF(pop=1,Sheet2!B3,IF(pop=2,Sheet2!E3,IF(pop=3,Sheet2!G3,Sheet2!I3)))","v":4.162}]
[]
["What is the second population?",{"$nulls":3},"Normal population",null,4]
[{"$nulls":4},"Uniform population"]
[{"$nulls":4},"U-shaped population"]
[{"$nulls":4},"Skewed population"]
[]
[]
[]
["What is the sample size n (2-50)?",null,null,{"$f":"E27","v":33},33]
[]
["The mean and standard deviation ",{"$nulls":3},"                  m =     ",{"$f":"IF(_pop2=1,Sheet2!B2,IF(_pop2=2,Sheet2!E2,IF(_pop2=3,Sheet2!G2,Sheet2!I2)))","v":71.19}]
[null,"of this population are:",null,null,"              s =",{"$f":"IF(_pop2=1,Sheet2!B3,IF(_pop2=2,Sheet2!E3,IF(_pop2=3,Sheet2!G3,Sheet2!I3)))","v":3.291}]
[]
["How many samples (50-250)?",null,null,{"$f":"E32","v":110},110]
[]
[]
[]
["According to statistical theory,"]
[null,"the mean of the differences of all sample means =",{"$nulls":3},{"$f":"F17-F29","v":{"v":-2.719999999999999,"d":"-2.72"}},{"$nulls":3},{"$f":"\"On \"&TEXT(flips,\"0\")&\" samples of size \"&TEXT(\"n\",\"\")&\"  = \"&TEXT(n,\"0\")& \" from the \" &TEXT(pop_name,\"\")& \" population:\"","v":"On 110 samples of size n  = 17 from the uniform population:"}]
[null,null,"                                with a standard deviation  =",null,null,{"$f":"IF(AND(n>30,nn>30),Sheet2!S56, Sheet2!S58)","v":1.0667932249661274},{"$nulls":3},{"$f":"\"          and of size \"&TEXT(\"n\",\"\")&\"  = \"&TEXT(nn,\"0\")& \" from the \" &TEXT(pop2_name,\"\")& \" population:\"","v":"          and of size n  = 33 from the skewed population:"}]
[{"$nulls":10},{"$f":"\"The mean of the differences of sample means =\"","v":"The mean of the differences of sample means ="},{"$nulls":3},{"$f":"SUM(Sheet2!AB2:AB251)/flips","v":{"v":-2.674801490844273,"d":"-2.67"}}]
[{"$nulls":10},"       The corresponding standard deviation =",{"$nulls":3},{"$f":"Sheet2!R26","v":{"v":1.061455525848844,"d":"1.061"}}]
[null,null,"Run a New Random Sample",null,false]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[null,null,"   Item 5"]
[null,null,"   Item 6"]
[]
[]
[]
["To access/download all the DIGMath Apps for Statistics"]
["Click this link:",null,"DIGMath for Statistics and Probability"]
[]
["Created by:  Sheldon P. Gordon   &   Florence S. Gordon   © 2025"]
["                  Farmingdale State College      NYIT"]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"Sheet2","index":1,"n_rows":428,"n_cols":29,"rows_kept":428}
[null,"Normal data",null,null,"Uniform data",null,"U-shaped",null,"Skewed data",{"$nulls":4},"Population 1 Samples",{"$nulls":3},"Pop'n 1 Histogram",{"$nulls":6},"Population 2 Samples",null,null,"Diff of Means"]
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