Question

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.

c. Suppose the true population mean change in score on one of the standardized tests for all students who paid a private tutor is 7. Which of the two​ tests, Mathematics or​ Verbal, is most likely to have this mean​change? Explain.

Choose the correct answer below.

A. Mathematics is more likely to have this true mean change because it falls within the​ 95% confidence interval for

Mathematics

B. Verbal is more likely to have this true mean change because it falls outside the​ 95% confidence interval for Verbal.

C. Verbal is more likely to have this true mean change because it falls within the​ 95% confidence interval for Verbal.

D. Mathematics is more likely to have this true mean change because it falls outside the​ 95% confidence interval for Mathematics.

E. Both are equally likely to have this true mean change because it falls within the​ 95% confidence interval for both Verbal and Math.

Answer 1