In a study on annual textbook expenditures by full-time economics students, a random sample of size n = 25 found average expenditures of X25 = $730 and sample variance S? = 22500. (a) Use the above information to construct a 90% confidence interval for the mean, u. | (b) With known variance o = 22500, test the hypothesis that the mean expenditure on textbooks by economics students is Ho = $668. Clearly state the hypotheses. Carry out tests at the a = .05 significance level. Find the p-value associated with this test. (c) Determine the probabilities of Type I and Type II errors under the tests in (c) if the true population mean is u* = 760 (o = 22500). %3D