Question

If we have a sample size of 100 and the estimate of the population proportion is 0.10, can we estimate the sampling distribution of p̂ with a normal distribution?

1) Yes
2) No

Answer 1

Yes, with a sample size of 100 and an estimated population proportion of 0.10, the sampling distribution of p̂ can be estimated with a normal distribution because both np and nq are greater than five. So, the correct option is 1) Yes

Step-by-step explanation:

To determine if we can estimate the sampling distribution of p̂ with a normal distribution when we have a sample size of 100 and the estimate of the population proportion is 0.10, we need to check if the sample meets certain criteria established by the central limit theorem for proportions.

Specifically, the sample size (n) multiplied by the estimated population proportion (p) and its complement (q = 1-p) must both be greater than 5 (np > 5 and nq > 5).

In the given scenario with p = 0.10 and n = 100, we have:

np = 100 * 0.10 = 10

nq = 100 * 0.90 = 90

Both np and nq exceed 5, which allows us to approximate the binomial distribution of the sample proportion with a normal distribution.

Thus, the answer to this question is:

Yes