Question

siness test before and after the course. The results are given below. 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). To test the effectiveness of a business school preparation course, 9 students took a general bu

Answer 1

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.

We use a paired sample ttest for this hypothesis. The details are given below.

(b) What assumption is necessary to perform the hypothesis test in (a)?
- The variable must be continous.
- Each observation must be independent of the other.
- The observations must be normally distributed.
- There must no outliers in the data.

(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?

We see that zero is part of the confidence interval, hence we fail to reject the null hypothesis and conclude that there is no evidence to support the claim that there is a difference in the test score before and after.

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

In both the test we fail to reject the null hypothesis.
Conclusion : At 0.01 level of significance, there is no evidence of a difference between before and after scores of the students.