Question

in a survey of 2521 adults, 1459 say they have started paying bills online in the last year.
construct a 99% confidence interval for the population proportion. interpret the results.
a 99% confidence interval for the population proportion is (0.554, 0.604).
(round to three decimal places as needed.)
interpret your results. choose the correct answer below.
○ a. with 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
○ b. with 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.
○ c. the endpoints of the given confidence interval show that adults pay bills online 99% of the time.

Explanation:

A confidence interval for a population proportion gives a range of values within which the true population proportion is likely to lie. A 99% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, about 99% of those intervals would contain the true population proportion. Option A is correct because the confidence interval is for the population proportion, not the sample proportion (eliminating B). Option C misinterprets the confidence level as a proportion of time, which is incorrect.

Answer:

A. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.