A school board wanted to see if reading test scores have changed in the past 10 years by testing a random sample of 15 students to see whether the reading scores are greater than the average score of 75 ten years ago. The scores of the sample are as follows:

63, 95, 81, 75, 90, 64, 45, 84, 90, 38, 76, 78, 50, 87, 92

a) State the appropriate hypotheses to test whether the reading scores are greater than expected.

b) Determine the mean and standard deviation of the sample of students' reading scores.

c) Test the hypotheses stated in part (a) at a 5% level of significance, and comment on your findings.