Question

College alcohol and drug use: In a Washington Post/Kaiser Family Foundation poll conducted from January through March 2015, 56% of adults (ages 17‐26) who attended college during the past 4 years say that alcohol and drug use at their school is a big problem. The 95% confidence interval is (0.53, 0.59).

Which of the following is an appropriate interpretation of the 95% confidence interval?

A)There is a 95% probability that the proportion of adults (ages 17‐26) who attended college during the past 4 years say that alcohol and drug use at their school is a big problem is between 53% and 59%.
B)We are 95% confident that the proportion of the sample who say that alcohol and drug use at their school is a big problem is between 53% and 59%.
C)Of random samples of the same size, 95% will have between 53% and 59% of respondents who say that alcohol and drug use at their school is a big problem.
D)We are 95% confident that the proportion of adults (ages 17‐26) who attended college during the past 4 years and say that alcohol and drug use at their school is a big problem is between 53% and 59%.

Answer:
D

Answer 1

D)We are 95% confident that the proportion of adults (ages 17‐26) who attended college during the past 4 years and say that alcohol and drug use at their school is a big problem is between 53% and 59%.

Explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

95% confidence interval is (0.53, 0.59).

This means that we are 95% sure that the true proportion for the population of adults who attended college who say that alcohol is a big problem is between 0.53 and 0.59. This means that the answer is given by option D.