Question

A research article included the following information:

In the sample of 50 students, 95% of SAT-Math scores were between 380 and 740.

A 95% confidence interval for the mean SAT-Math score in the population was computed to be [532, 588].

Your friend, who has never taken a statistics course, is confused as to how these two statements are different.

Explain how these two statements are different in a way that your friend, with no experience with statistics, can understand.

Answer 1

The first statement talks about the actual scores, while the second one talks about the average score.

In the sample of 50 students, 95% of SAT-Math scores were between 380 and 740.

This statement means that 95% of the student scores in SAT-Math is between 380 and 740.

A 95% confidence interval for the mean SAT-Math score in the population was computed to be [532, 588].

This statement means that we are 95% sure that the true mean(average) of SAT-Math scores is between 532 and 588.