Which statistical test is used to determine if flea rates differ significantly between dogs and cats?

Which statistical test is used to determine if flea rates differ significantly between dogs and cats?

• A. Chi-square test for independence
• B. Paired t-test
• C. One-sample z-test
• D. 2-proportion z-test

Answer: (D)

The essential idea here is comparing two proportions from independent groups. Flea infestation is a binary outcome (yes or no) for each animal, and you have two separate groups (dogs and cats). The goal is to test whether the infestation rate in dogs differs from the infestation rate in cats. The two-proportion z-test does exactly that: it compares the observed proportions p1 (dogs) and p2 (cats) to see if the difference could plausibly be zero under the null hypothesis of equal rates. It uses the pooled proportion under that null to compute a z statistic, which, with a large enough sample, follows a standard normal distribution. If the computed z is large in magnitude, you conclude the flea rates differ between the two species. This choice is the most direct for this scenario. The paired t-test wouldn’t apply because the data aren’t paired and the outcome isn’t a continuous measure. The one-sample z-test compares a single group to a known proportion, not two groups. A chi-square test for independence could also be used on a 2x2 table of infestation by species and would yield similar conclusions in large samples, but the two-proportion approach targets the specific comparison of the two rates directly, making it the best fit here.

The essential idea here is comparing two proportions from independent groups. Flea infestation is a binary outcome (yes or no) for each animal, and you have two separate groups (dogs and cats). The goal is to test whether the infestation rate in dogs differs from the infestation rate in cats.

The two-proportion z-test does exactly that: it compares the observed proportions p1 (dogs) and p2 (cats) to see if the difference could plausibly be zero under the null hypothesis of equal rates. It uses the pooled proportion under that null to compute a z statistic, which, with a large enough sample, follows a standard normal distribution. If the computed z is large in magnitude, you conclude the flea rates differ between the two species.

This choice is the most direct for this scenario. The paired t-test wouldn’t apply because the data aren’t paired and the outcome isn’t a continuous measure. The one-sample z-test compares a single group to a known proportion, not two groups. A chi-square test for independence could also be used on a 2x2 table of infestation by species and would yield similar conclusions in large samples, but the two-proportion approach targets the specific comparison of the two rates directly, making it the best fit here.