Question

in a survey of 2059 adults in a recent year, 724 made a new years resolution to eat healthier. 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 (0.335, 0.369) (round to three decimal places as needed.) the 95% confidence interval for the population proportion p is (0.331, 0.373) (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 to eat healthier 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 are the same width. d. the confidence intervals cannot be compared

Explanation:

Step1: Calculate width of 90% confidence interval

Width = \(0.369 - 0.335=0.034\)

Step2: Calculate width of 95% confidence interval

Width = \(0.373 - 0.331 = 0.042\)

Step3: Compare widths

Since \(0.042>0.034\)

Answer:

B. The 95% confidence interval is wider.