Question

in a survey of 2267 adults in a recent year, 1419 say they have made a new years resolution. construct 90% and 95% confidence intervals for the population proportion. interpret the results and compare the widths of the confidence intervals. the 90% confidence interval for the population proportion p is (0.609, 0.643). (round to three decimal places as needed.) the 95% confidence interval for the population proportion p is (0.606, 0.646). (round to three decimal places as needed.) with the given confidence, it can be said that the population proportion of adults who say they have made a new years resolution is between the endpoints of the given confidence interval. compare the widths of the confidence intervals. choose the correct answer below. a. the 90% confidence interval is wider. b. the 95% confidence interval is wider. c. the confidence intervals cannot be compared. d. the confidence intervals are the same width.

Explanation:

Step1: Calculate the width of 90% confidence interval

Width of 90% confidence interval = \(0.643 - 0.609=0.034\)

Step2: Calculate the width of 95% confidence interval

Width of 95% confidence interval = \(0.646 - 0.606 = 0.04\)

Step3: Compare the widths

Since \(0.04>0.034\), the 95% confidence interval is wider.

Answer:

B. The 95% confidence interval is wider.