Question

For the binomial sample information summarized below, indicate whether the sample size is large enough to use the large sample approximation to construct a confidence interval for p. n=400, p=0.18. Is the sample size large enough?

a) Yes
b) No

Answer 1

Yes, the sample size is large enough to use the large sample approximation to construct a confidence interval for p, since both np (72) and nq (328) are greater than 5.

Step-by-step explanation:

The student is asking whether the sample size is large enough to use the large sample approximation to construct a confidence interval for a proportion p, given that n = 400 and p = 0.18. This question is related to statistics, a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of masses of numerical data.

To determine if the large sample approximation can be used, we look at the product of the sample size (n) and the sample proportion (p), as well as the product of the sample size (n) and the complement of the sample proportion (q = 1 - p). The rule of thumb suggests that for the approximation to be appropriate, both np and nq should be greater than 5.

In this case: np = 400 * 0.18 = 72 and nq = 400 * (1-0.18) = 400 * 0.82 = 328. Since both np and nq are greater than 5, we can say that the sample size is large enough to use the large sample approximation for constructing a confidence interval for p.