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The results of a study of 258 students who paid a private tutor to help them...

The results of a study of 258 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

Mean change in score

18

8

Standard deviation of score changes

67

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.

(__________,___________)

​(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 is one of the end points 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 lies at the mean 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.

(________,_______)

​(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 Verbal score is one of the end points of the above interval.

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

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

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

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