1. (30p.) The heights of a random sample of 64 college students showed a mean of 169 centimeters and a standard deviation of 8 centimeters. a. Construct a 98% confidence interval for the mean height of all college students. b. Construct a 98% prediction interval for a single observed height. c. Perform t-tests for the hypotheses below i. $H_0: \mu = 170$ against $H_1: \mu \ne 170$ ii. $H_0: \mu = 170$ against $H_1: \mu < 170$ iii. $H_0: \mu = 180$ against $H_1: \mu < 180$ Assume a significance level $\alpha = 2\%$. Calculate the t-values and p-values. Interpret the results of the tests.
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