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Chapter 10 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