Question

In a large population, 67% of the households have cable tv. A simple random sample of 256 households is to be contacted and the sample proportion computed. What is the mean and standard deviation of the sampling distribution of the sample proportions?

Answer 1

Answer:
`\mu_{\hat{p}}=0.67`

`\sigma_{\hat{p}}=0.029`

Explanation:

The mean and standard deviation of the sampling distribution of the sample proportions is given by :-

`\mu_{\hat{p}}=p`

`\sigma_{\hat{p}}=\sqrt{(p(1-p))/(n)}` , where n is the sample size and p is the population proportion.

Given : p= 0.67 and n= 256

Then, the mean and standard deviation of the sampling distribution of the sample proportions is given by :-

`\mu_{\hat{p}}=0.67`

`\sigma_{\hat{p}}=\sqrt{(0.67(1-0.67))/(256)}\\\\=0.0293882948638\approx0.029`