Chapter 7, Problem 7.2P

a. The students at Littlewood Regional High School cut an average of 3.3 classes per month. A random sample of 117 seniors averages 3.8 cuts per month, with a standard deviation of 0.53. Are seniors significantly different from the student body as a whole? (HINT: The wording of the research question suggests a two-tailed test. This means that the alternative, or research, hypothesis in step 2 will be stated as $H_1:\mu \ne 3.3$ and that the critical region will be split between the upper and lower tails of the sampling distribution. See Table 7.3 for values of Z(critical) for various alpha levels.)

b. What if the research question were changed to "Do seniors cut a significantly greater number of classes"? How would the test conducted in problem 7.2a change? (HINT: This wording implies a one-tailed test of significance. How would the research hypothesis change? For the alpha you used in problem 7.2a, what would the value of Z(critical) be?)