Chapter 15.1, Problem 2SE

Instructions: For each exercise, include software results (e.g., from Excel, MegaStat, or JMP) to support your chi-square calculations. (a) State the hypotheses. (b) Show how the degrees of freedom are calculated for the contingency table. (c) Using the level of significance specified in the exercise, find the critical value of chi-square from Appendix E or from Excel’s function =CHISQ.INV.RT(alpha, deg_freedom). (d) Carry out the calculations for a chi-square test for independence and draw a conclusion. (e) Which cells of the contingency table contribute the most to the chi-square test statistic? (f) Are any of the expected frequencies too small? (g) Interpret the p-value. If necessary, you can calculate the p-value using Excel’s function =CHISQ.DIST.RT(test statistic, deg_freedom). *(h) If it is a 2 × 2 table, perform a two-tailed, two-sample z test for π₁ = π₂ and verify that z² is the same as your chi-square statistic. Note: Exercises marked with an asterisk (*) are more difficult.

15.2 Teenagers make up a large percentage of the market for clothing. Below are data on running shoe ownership in four world regions (excluding China). Research question: At α = .01, does this sample show that running shoe ownership depends on world region? (See J. Paul Peter and Jerry C. Olson, Consumer Behavior and Marketing Strategy, 9th ed. [McGraw-Hill, 2004], p. 64.)