Assume that the mean height for women at a large American university (to be viewed as a population) is 65 inches with a standard deviation of 3 inches.

a. If the women are placed randomly into physical education classes of 36 each, what will be the SD of the class means for height (i.e., the standard error of the mean)?

b. Using your answer to part (a), what is the z score for a phys ed class whose average height is 64.2 inches? What are the one- and two-tailed p values for this class?

c. If you were testing the null hypothesis (i.e., μ = 65), would you reject H₀ for the class in part b, at the .05 level for a one-tailed test? For a two-tailed test?

d. Repeat part (b) for a class whose mean height is 67.4 inches. Would you reject the null hypothesis for this class with a two-tailed test at the .05 level? At the .01 level?