11.82 Multiple response variables Each subject in a sample of 100 men and 100 women is asked to indicate which of the following factors (one or more) are responsible for increases in crime committed by teenagers: A—the increasing gap in income between the rich and poor, B—the increase in the percentage of single-parent families, C—insufficient time that parents spend with their children. To analyze whether responses differ by gender of respondent, we cross-classify the responses by gender, as the table shows.

a. Is it valid to apply the chi-squared test of independence to these data? Explain.

b. Explain how this table actually provides information needed to cross-classify gender with each of three variables. Construct the contingency table relating gender to opinion about whether factor A is responsible for increases in teenage crime.

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Three Factors for Explaining Teenage Crime Gender Men Women A B C 58 60 81 75 75 87 86