Chapter 15.1, Problem 4SE

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.

15.4 Is HDTV ownership related to quantity of purchases of other electronics? A Best Buy retail outlet collected the following data for a random sample of its recent customers. Research question: At α = .10, is the frequency of in-store purchases independent of the number of large-screen HDTVs owned (defined as 50 inches or more)?