Question

in a survey of 3333 adults, 1474 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 (0.420, 0.464) (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 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. b. 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. 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 estimates the range within which the true population proportion lies. 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 incorrect because it refers to the sample proportion (we are interested in the population proportion). Option C misinterprets the confidence level - it's not about the frequency of paying bills but about the confidence in capturing the population proportion. Option B is correct as it correctly states that with 99% confidence, the population proportion is within the interval endpoints.

Answer:

B. 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.