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Please show work and explain. To test the effectiveness of a business school preparation course, 9...

Please show work and explain.

To test the effectiveness of a business school preparation course, 9 students took a general business test before and after the course. The results:

Student

Exam Score

Before the Course

Exam Score

After the Course

1

630

770

2

690

770

3

910

1,000

4

750

710

5

450

550

6

840

860

7

820

770

8

630

610

9

580

585

(a) Use an appropriate hypothesis test, at 0.01 level of significance, to determine whether there is evidence of a difference between before and after scores of the students.

(b) What assumption is necessary to perform the hypothesis test in (a)?

(c) Construct a 99% confidence interval estimate of the mean difference in before and after scores. Interpret the interval. What is your decision based on this confidence interval estimate?

(d) Compare the results in (a) and (c).

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