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%.
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%.
Step-by-step 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.
After graphing the set of inequalities and looking for the overlapping of the shading, the only ordered pair that falls within this shaded area is ( -2, 2)
