The results of a study of 270

students who paid a private tutor to help them improve their scores on a standardized test are shown below. The changes in both the Mathematics and Verbal scores for these students are reproduced in the table. Complete parts a through c below.

Test score improvements

Math

Verbal

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Mean change in score

20

5

Standard deviation of score changes

63

50

a. Construct and interpret a 95% confidence interval for the population mean change in the Mathematics score for students who pay a private tutor.

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(Round to three decimal places as needed.)

Interpret this interval. Choose the correct answer below.

A.

One can be 95% confident the true mean change in the Mathematics score lies at the mean of the above interval.

B.

There is a 95% probability that the true mean change in the Mathematics score is the mean of the interval.

C.

One can be 95% confident the true mean change in the Mathematics score is one of the end points of the above interval.

D.

One can be 95% confident the true mean change in the Mathematics score lies within the above interval.

b. Construct and interpret a 95% confidence interval for the population mean change in the Verbal score for students who pay a private tutor.

left parenthesis nothing comma nothing right parenthesis,

(Round to three decimal places as needed.)