Question

In a survey of 2347 adults, 723 say they believe in UFOs. Construct a 95% confidence interval for the population proportion of adults who believe in UFOs.

A 95​% confidence interval for the population proportion is (___,____) ​(Round to three decimal places as​ needed.)

A. With 95​% ​confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

B. The endpoints of the given confidence interval shows that 95​% of adults believe in UFOs.

C. With 95​% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

D. With 95​% ​probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval.

Answer 1

p̂ = X / n = 723/2347 = 0.308
p̂ ± Z(α/2) √( (p * q) / n)
0.3081 ± Z(0.05/2) √( (0.3081 * 0.6919) / 2347)
Z(α/2) = Z(0.05/2) = 1.96
Lower Limit = 0.308 - Z(0.05) √( (0.3081 * 0.6919) / 2347) = 0.289
upper Limit = 0.308 + Z(0.05) √( (0.3081 * 0.6919) / 2347) = 0.327
95% Confidence interval is ( 0.289 , 0.327 )

With 95​% ​confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.