Question

In a large population, 91% of the households have cable tv. A simple random sample of 144 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 with explanation:

We are given that $\hat{p}=0.91$

Sample size : $n=144$

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

$\mu_{\hat{p}}=p=0.91$

The mean of the sampling distribution of the sample proportions is 0.91

The standard deviation of the sampling distribution of the sample proportions :

$\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}\\\\=\sqrt{\dfrac{0.91(1-0.91)}{144}}=0.0238484800354\approx0.0238$

Hence, the standard deviation of the sampling distribution of the sample proportions is 0.0238