Among college-age drivers, 5% of the 576 men said they had been ticketed for speeding during the past year, compared to only 3% of the 552 women. Does this indicate a significant difference between college males and females in terms of being ticketed for speeding?

Among college-age drivers, 5% of the 576 men said they had been ticketed for speeding during the past year, compared to only 3% of the 552 women. Does this indicate a significant difference between college males and females in terms of being ticketed for speeding?

• A. Chi-square test of independence
• B. 2-proportion z-test
• C. Paired t-test
• D. ANOVA

Answer: (B)

You’re testing whether two independent proportions differ. Here, college-age men and women are two independent groups, and the outcome—being ticketed for speeding—is binary (yes or no). With large samples, the difference between the two sample proportions is approximately normally distributed, so the standard way to assess whether the proportions differ is a two-proportion z-test. This test directly answers: is p1 equal to p2, where p1 is the proportion of men ticketed and p2 is the proportion of women ticketed? Using the observed proportions (0.05 for men and 0.03 for women) and their sample sizes (576 and 552), you compute a z statistic to determine if the observed difference is statistically significant at your chosen alpha level. A chi-square test of independence could be used on the 2x2 table of gender by speeding-ticket status, but the two-proportion z-test is the standard direct approach for comparing two specific proportions. The other options aren’t appropriate here: a paired t-test is for related or matched data, and ANOVA is for comparing means across groups rather than proportions.

You’re testing whether two independent proportions differ. Here, college-age men and women are two independent groups, and the outcome—being ticketed for speeding—is binary (yes or no). With large samples, the difference between the two sample proportions is approximately normally distributed, so the standard way to assess whether the proportions differ is a two-proportion z-test. This test directly answers: is p1 equal to p2, where p1 is the proportion of men ticketed and p2 is the proportion of women ticketed? Using the observed proportions (0.05 for men and 0.03 for women) and their sample sizes (576 and 552), you compute a z statistic to determine if the observed difference is statistically significant at your chosen alpha level.

A chi-square test of independence could be used on the 2x2 table of gender by speeding-ticket status, but the two-proportion z-test is the standard direct approach for comparing two specific proportions. The other options aren’t appropriate here: a paired t-test is for related or matched data, and ANOVA is for comparing means across groups rather than proportions.