Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Business Statistics, 4e by Ken Black Chapter 10 Statistical Inferences about Two Populations

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Learning Objectives Test hypotheses and construct confidence intervals about the difference in two population means using the Z statistic. Test hypotheses and construct confidence intervals about the difference in two population means using the t statistic.

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Learning Objectives Test hypotheses and construct confidence intervals about the difference in two related populations. Test hypotheses and construct confidence intervals about the differences in two population proportions. Test hypotheses and construct confidence intervals about two population variances.

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Sampling Distribution of the Difference Between Two Sample Means Population 1 Population 2

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Sampling Distribution of the Difference between Two Sample Means

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Z Formula for the Difference in Two Sample Means When  1 2 and  2 2 are known and Independent Samples

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hypothesis Testing for Differences Between Means: The Wage Example (part 1) Rejection Region Non Rejection Region Critical Values Rejection Region H H o a : :    

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hypothesis Testing for Differences Between Means: The Wage Example (part 2) Rejection Region Non Rejection Region Critical Values Rejection Region 0

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hypothesis Testing for Differences Between Means: The Wage Example (part 3) Advertising Managers Auditing Managers

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hypothesis Testing for Differences between Means: The Wage Example (part 4) Rejection Region Non Rejection Region Critical Values Rejection Region 0

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Difference Between Means: Using Excel z-Test: Two Sample for Means Adv MgrAuditing Mgr Mean Known Variance Observations3234 Hypothesized Mean Difference0 z2.35 P(Z<=z) one-tail z Critical one-tail1.64 P(Z<=z) two-tail z Critical two-tail1.960

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 10.1 (part 1) Non Rejection Region Critical Value Rejection Region 0

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 10.1 (part 2) Non Rejection Region Critical Value Rejection Region 0

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Confidence Interval to Estimate  1 -  2 When  1,  2 are known

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 10.2

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons The t Test for Differences in Population Means Each of the two populations is normally distributed. The two samples are independent. The values of the population variances are unknown. The variances of the two populations are equal.  1 2 =  2 2

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons t Formula to Test the Difference in Means Assuming  1 2 =  2 2

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hernandez Manufacturing Company (part 1) Rejection Region Non Rejection Region Critical Values Rejection Region 0

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hernandez Manufacturing Company (part 2) Training Method A Training Method B

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hernandez Manufacturing Company (part 3)

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons MINITAB Output for Hernandez New-Employee Training Problem Twosample T for method A vs method B NMeanStDevSE Mean method A method B % C.I. for mu method A - mu method B: (-12.2, -5.3) T-Test mu method A = mu method B (vs not =): T = P= DF = 25 Both use Pooled StDev = 4.35

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons EXCEL Output for Hernandez New-Employee Training Problem t-Test: Two-Sample Assuming Equal Variances Variable 1Variable 2 Mean Variance Observations1512 Pooled Variance Hypothesized Mean Difference0 df25 t Stat P(T<=t) one-tail1.12E-05 t Critical one-tail1.71 P(T<=t) two-tail2.23E-05 t Critical two-tail 2.06

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Confidence Interval to Estimate  1 -  2 when  1 2 and  2 2 are unknown and  1 2 =  2 2

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Dependent Samples Before and after measurements on the same individual Studies of twins Studies of spouses Individual Before After

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Formulas for Dependent Samples

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons P/E Ratios for Nine Randomly Selected Companies Company2001 P/E Ratio2002 P/E Ratio

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hypothesis Testing with Dependent Samples: P/E Ratios for Nine Companies Rejection Region Non Rejection Region Critical Value 0 Rejection Region

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hypothesis Testing with Dependent Samples: P/E Ratios for Nine Companies Company 2001 P/E Ratio 2002 P/E Ratiod

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hypothesis Testing with Dependent Samples: P/E Ratios for Nine Companies

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hypothesis Testing with Dependent Samples: P/E Ratios for Nine Companies t-Test: Paired Two Sample for Means 2001 P/E Ratio 2002 P/E Ratio Mean Variance Observations99 Pearson Correlation0.674 Hypothesized Mean Difference0 df8 t Stat-0.7 P(T<=t) one-tail0.252 t Critical one-tail1.86 P(T<=t) two-tail0.504 t Critical two-tail2.306

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hypothesis Testing with Dependent Samples: Demonstration Problem 10.5 Individual Before After d

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hypothesis Testing with Dependent Samples: Demonstration Problem 10.5 Rejection Region Non Rejection Region Critical Value 0

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Hypothesis Testing with Dependent Samples: Demonstration Problem 10.5

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Confidence Intervals for Mean Difference for Related Samples

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Difference in Number of New-House Sales RealtorMay 2001May 2002d

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Confidence Interval for Mean Difference in Number of New-House Sales

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Sampling Distribution of Differences in Sample Proportions

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Z Formula for the Difference in Two Population Proportions

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Z Formula to Test the Difference in Population Proportions

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Testing the Difference in Population Proportions (Demonstration Problem 10.6) Rejection Region Non Rejection Region Critical Values Rejection Region 0

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Testing the Difference in Population Proportions (Demonstration Problem 10.6)

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Confidence Interval to Estimate p 1 - p 2

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Example Problem: When do men shop for groceries?

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons F Test for Two Population Variances

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons F Distribution with 1 = 10 and 2 = 8

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons A Portion of the F Distribution Table for  = Numerator Degrees of Freedom Denominator Degrees of Freedom

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Sheet Metal Example: Hypothesis Test for Equality of Two Population Variances (Part 1)

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Sheet metal Manufacturer (Part 2) Rejection Regions Critical Values Non Rejection Region

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Sheet Metal Example (Part 3) Machine Machine