Question

Students were given a pre-test. Then after they listened to a certain type of music they were given a similar post test. If we define the difference as the post test score minus the pre test score and we find a 95% confidence interval for the mean of the differences to be [-1.34, 4.56]. Which of the following is true? It seems like music has affected the scores and the post test scores are significantly higher. It seems like music has affected the scores and the post test scores are significantly lower. There seems to be insufficient evidence to show that music affected the scores since zero is in the confidence interval. The average scores in the post test were on average about 4.56 points higher than the pre-test.

Answer 1

x :- post-test score; y:- pre-test score

d= the difference as the post-test score minus the pre-test score= x-y

if both scores are equal then d= 0 .

If post-test scores are greater than the pre-test score then d > 0.

if post-test scores are less than the pre-test score then d <  0.

The 95% confidence interval for the mean of the differences to be [-1.34, 4.56]

from confidence interval, if it contains 0 then both have the same scores.

Here confidence interval contains 0 (-1.34, 4.56) .so we can say that both scores are the same.

I.e music does not have any impact on test scores.

Answer:-

There seems to be insufficient evidence to show that music affected the scores since zero is in the confidence interval.