The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university's record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. Required:
a. State the null and alternative hypotheses for this study.
b. What critical value should the president use to determine the rejection region?
c. What is the value of the test statistic?
d. What is the p value of the test?
e. What is your conclusion