Question

in a survey of 2350 adults, 723 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 (0.284, 0.333). (round to three decimal places as needed.) interpret your results. choose the correct answer below. a. the endpoints of the given confidence interval shows that 99% of adults believe in ufos. b. with 99% probability, the population proportion of adults who do not believe in ufos is between the endpoints of the given confidence interval. c. 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. 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.

Explanation:

A confidence interval gives a range within which the population parameter (here, the proportion of adults who believe in UFOs) is likely to lie. A 99% confidence interval means that if we were to take many samples and construct confidence intervals, about 99% of them would contain the true population proportion.

• Option A is wrong because the confidence interval is about the population proportion, not that 99% of adults believe (the proportion within the interval is an estimate, not a statement about the percentage of adults).
• Option B is wrong as it refers to the proportion of adults who do not believe, while the confidence interval is for those who believe.
• Option C is wrong because it refers to the sample proportion (the sample proportion is used to calculate the confidence interval, but the confidence interval is for the population proportion).
• Option D is correct as it correctly states that with 99% confidence, the population proportion of adults who believe in UFOs is within the given confidence interval.

Answer:

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.