Question

A veterinarian believes the proportion of cats that are expected to live more than 15 years to be less than 30%. What sample size should the veterinarian use to achieve a margin of error of no more than 0.07% for a 99.7% confidence interval using the empirical rule? Use p=0.5 since we do not know the exact population proportion.

A) 324

B) 384

C) 456

D) 512

Answer 1

To achieve a margin of error of no more than 0.07% for a 99.7% confidence interval using the empirical rule, the veterinarian should use a sample size of 512.

Step-by-step explanation:

To find the sample size needed for a 99.7% confidence interval using the empirical rule, we need to determine the z-score that corresponds to a confidence level of 99.7%. Since the confidence interval is symmetrical, we can use the formula z = 3 for a 99.7% confidence level.

Next, we need to determine the margin of error. The margin of error is given by the formula margin of error = z * sqrt(p * (1-p) / n), where p is the estimated proportion and n is the sample size.

In this case, we want the margin of error to be no more than 0.07%. Plugging in the values, we have 0.0007 = 3 * sqrt(0.5 * (1-0.5) / n). Solving for n, we get n = (3^2 * 0.5 * (1-0.5)) / (0.0007^2) = 512.

Therefore, the veterinarian should use a sample size of 512.