A NYC mayoral candidate asks voters from two boroughs about approval of Stop and Frisk. Do approval rates vary between Queens and Brooklyn?

A NYC mayoral candidate asks voters from two boroughs about approval of Stop and Frisk. Do approval rates vary between Queens and Brooklyn?

• A. One-Proportion Z-Test
• B. Two-Proportion Z-Test
• C. Two-Proportion Z-Test
• D. Chi-Square Test for Independence

Answer: (C)

Comparing two independent sample proportions to see if they differ. In this scenario you’re looking at approval rates from voters in two different boroughs, with a binary outcome (approve or not). The question asks whether the proportion approving Stop and Frisk is the same in Queens and Brooklyn, so the method should directly compare two proportions. A two-proportion z-test fits because it tests whether p1 equals p2 for two independent groups. You’d take the observed approval rates from each borough, use the pooled proportion under the null hypothesis that there is no difference, compute the standard error for the difference in proportions, and calculate a z-statistic to see if the observed difference is likely due to chance. This approach relies on large-sample approximations, so you need reasonably large counts in both boroughs (enough successes and non-successes in each group). If those conditions aren’t met, other approaches like exact methods or a chi-square test for independence in a 2x2 table could be considered, but the two-proportion z-test is the most direct way to assess whether the two proportions differ.

Comparing two independent sample proportions to see if they differ. In this scenario you’re looking at approval rates from voters in two different boroughs, with a binary outcome (approve or not). The question asks whether the proportion approving Stop and Frisk is the same in Queens and Brooklyn, so the method should directly compare two proportions.

A two-proportion z-test fits because it tests whether p1 equals p2 for two independent groups. You’d take the observed approval rates from each borough, use the pooled proportion under the null hypothesis that there is no difference, compute the standard error for the difference in proportions, and calculate a z-statistic to see if the observed difference is likely due to chance. This approach relies on large-sample approximations, so you need reasonably large counts in both boroughs (enough successes and non-successes in each group). If those conditions aren’t met, other approaches like exact methods or a chi-square test for independence in a 2x2 table could be considered, but the two-proportion z-test is the most direct way to assess whether the two proportions differ.