Question

In a survey of 2331 ​adults, 711 say they believe in UFOs. Construct a 99 % confidence interval for the population proportion of adults who believe in UFOs. A 99​% confidence interval for the population proportion is ​( nothing​, nothing​). ​(Round to three decimal places as​ needed.) Interpret your results. Choose the correct answer below. A. With 99​% ​probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval. B. With 99​% ​confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval. C. The endpoints of the given confidence interval shows that 99​% of adults believe in UFOs. D. With 99​% ​confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

Answer 1

sample proportion, = 0.305
sample size, n = 2331
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.305 * (1 - 0.305)/2331) = 0.0095

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.305 - 2.58 * 0.0095 , 0.305 + 2.58 * 0.0095)
CI = (0.280 , 0.330)

With 99​%​confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.