Question

A recent survey of 35,101 randomly selected U.S. adults studied the religious affiliation of Americans. The survey interviewed 245 people in Maine. Suppose that this is a simple random sample of adult residents of Maine. Of these 245 people, 56 said they attend religious services at least once a week. A 95% confidence interval for the proportion of all residents of Maine who attend religious services at least once a week is closest to

Answer 1

Answer: (0.177,0.283)

Step-by-step explanation:

Given : Sample size : $n= 245$

The proportion of adult said they attend religious services at least once a week : $p=\dfrac{56}{245}\approx0.23$

Significance level : $\alpha: 1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

The confidence interval for population proportion is given by :-

$p\pm\ z_{\alpha/2}\ \sqrt{\dfrac{p(1-p)}{n}}\\\\=0.52\pm(1.96)\sqrt{\dfrac{0.23(1-0.23)}{245}}\\\\\approx0.23\pm0.053=(0.23-0.053,0.23+0.053)=(0.177,0.283)$

Hence, the 95% confidence interval for the proportion of all residents of Maine who attend religious services at least once a week is (0.177,0.283).