Question

in a survey of 2542 adults in a recent year, 1301 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 (0.496, 0.528). (round to three decimal places as needed.) the 95% confidence interval for the population proportion p is (0.492, 0.532). (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 are the same width. d. the confidence intervals cannot be compared.

Explanation:

Step1: Calculate the width of 90% confidence interval

The width of a confidence interval for proportion is \(upper - lower\). For 90% confidence interval, width \(=0.528 - 0.496=0.032\)

Step2: Calculate the width of 95% confidence interval

For 95% confidence interval, width \(=0.532 - 0.492 = 0.04\)

Answer:

B. The 95% confidence interval is wider.