Question

In the 2008 General Social Survey, participants were asked: “To what extent do you consider yourself a religious person?” Of 2023 surveyed, 317 responded: “not at all.”

(a) Construct a 95% confidence interval for the true proportion of US adults who would respond “not at all” to this question.

(b) What is the margin of error for your confidence interval?

(c) How large would the sample need to be to obtain a margin of error of ±1%?

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 317 / 2023 = 0.157

Z_/2 = 1.96

(b)

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.157 * 0.843) / 2023)

= 0.016

(a)

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.157 - 0.016 < p < 0.157 + 0.016

0.141 < p < 0.173

The 95% confidence interval for the population proportion p is : (0.141 , 0.173)

(c)

= 0.157

1 - = 0.843

margin of error = E = 0.01

Z_/2 = 1.96

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (1.96 / 0.01)² * 0.157 * 0.843

= 5085

sample size = n = 5085