5. In order to improve the grades of students at UTC, several incentive programs

have been introduced. Results of random samples of grades from after and before

the incentive programs are given below. Assume the two populations are normally

distributed.

After Incentives

Before Incentives

Sample Size

14

12

Sample Mean

2.85

2.61

Sample Standard

Deviation

.40

.35

Sample Mode

2.5

3.0

a. Give the hypotheses.

b. Compute the test statistic.

c. Using a .10 level of significance, test to determine whether the incentive programs have significantly increased the average grades

d. Find the difference and discuss your results

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