A 2009 survey reported that 63% of dog owners and 53% of cat owners would be at least somewhat likely to give CPR to their pet. Which statistical test is appropriate to compare these two proportions?

A 2009 survey reported that 63% of dog owners and 53% of cat owners would be at least somewhat likely to give CPR to their pet. Which statistical test is appropriate to compare these two proportions?

• A. Fisher's exact test
• B. 2-proportion z-test
• C. Paired t-test
• D. One-sample z-test

Answer: (B)

The test is designed to compare two independent proportions to see if their difference is beyond what random variation would produce. When you have two large samples of yes/no responses (would give CPR to a pet) from distinct groups (dog owners vs cat owners), you model each group with a binomial distribution and test H0 that the true proportions are equal. The two-proportion z-test uses the difference between the observed sample proportions and checks how likely that difference is under the assumption of a common proportion. With large samples, the difference in proportions is approximately normal, so you compute a z-statistic (often with a pooled proportion under the null) and compare it to a standard normal to get a p-value. This makes it the appropriate method for this scenario. Fisher’s exact test is reserved for small samples or sparse counts in a 2x2 table, where the exact distribution is needed. A paired t-test is for matched or paired observations, not independent groups. A one-sample z-test would test a single group against a known proportion, not compare two groups.

The test is designed to compare two independent proportions to see if their difference is beyond what random variation would produce. When you have two large samples of yes/no responses (would give CPR to a pet) from distinct groups (dog owners vs cat owners), you model each group with a binomial distribution and test H0 that the true proportions are equal. The two-proportion z-test uses the difference between the observed sample proportions and checks how likely that difference is under the assumption of a common proportion. With large samples, the difference in proportions is approximately normal, so you compute a z-statistic (often with a pooled proportion under the null) and compare it to a standard normal to get a p-value. This makes it the appropriate method for this scenario.

Fisher’s exact test is reserved for small samples or sparse counts in a 2x2 table, where the exact distribution is needed. A paired t-test is for matched or paired observations, not independent groups. A one-sample z-test would test a single group against a known proportion, not compare two groups.