Chapter 15.1, Problem 3SE

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.

15.3 Students applying for admission to an MBA program must submit scores from the GMAT test, which includes a verbal and a quantitative component. Shown here are raw scores for 100 randomly chosen MBA applicants at a Midwestern, public, AACSB-accredited business school. Research question: At α = .005, is the quantitative score independent of the verbal score?