Question

Suppose we take repeated random samples of 50 college students from the same population and determine a 95% confidence interval for the mean GPA from each sample. Which of the following statements is true regarding the confidence intervals?

A. The intervals are centered around the population mean GPA.
B. The intervals are centered around the sample mean GPA.
C. 95% of the intervals will contain the sample mean in the long run.
D. 95% of the intervals will contain the population mean in the long run.

Answer 1

B. The intervals are centered around the sample mean GPA.

D. 95% of the intervals will contain the population mean in the long run.

Explanation:

Confidence interval:

Depends on two things: The sample mean and the margin of error.

Lower end: Sample mean - margin of error

Upper end: Sample mean + margin of error

This means that the intervals are centered around the sample mean.

x% level:

x% of the intervals will contain the population mean in the long run.

So the true statements are:

B. The intervals are centered around the sample mean GPA.

D. 95% of the intervals will contain the population mean in the long run.