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)

Explanation:

Given : Sample size :
`n= 245`

The proportion of adult said they attend religious services at least once a week :
`p=(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{(p(1-p))/(n)}\\\\=0.52\pm(1.96)\sqrt{(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).