Question

For a certain population of men, 8 percent carry a certain genetic trait. For a certain population of women, 0.5 percent carry the same genetic trait. Let pˆ1 represent the sample proportion of randomly selected men from the population who carry the trait, and let pˆ2 represent the sample proportion of women from the population who carry the trait. For which of the following sample sizes will the sampling distribution of pˆ1−pˆ2 be approximately normal?

Answer 1

The sampling distribution of ā-Ă will be approximately normal when both populations satisfy the conditions for np > 5 and nq > 5. The sample sizes must ensure these inequalities are met using the proportions 0.08 for men and 0.005 for women.

Step-by-step explanation:

The sampling distribution of ā - Ă will be approximately normal when the sample sizes are large enough to satisfy the condition np > 5 and nq > 5 for both populations. Given that in the population of men, 8 percent carry the genetic trait (p1 = 0.08), and in the population of women, 0.5 percent carry the trait (p2 = 0.005), we need to find appropriate sample sizes for each population.

For the men's population:
n1p1 > 5 and n1(1 - p1) > 5.

For the women's population:
n2p2 > 5 and n2(1 - p2) > 5.

The sample sizes should be selected in a way that these inequalities are met for both populations to ensure that the sampling distribution of ā-Ă is approximately normal.

Answer 2

D

Step-by-step explanation:

200 men and 2,000 women

i dont know how but that was just the answer