Solve hand written and show work

3. Consider the null hypothesis that the average weight of male students in a certain college is 68 kilograms against the alternative hypothesis that it is unequal to 68. Ho: ,u = 68: Ha: y at 68. If the rejection region is J? 69; Assume the standard deviation of the population of weights to be a = 3.2. (a) With a random sample of size n = 16, calculate Type I error and Type 11 error (assuming pt = 69 when calculating Type 11 error). (15 points) (in) How many samples are needed to achieve a Type 11 error when p = 69 is 0.1 and Type I error is 0.1? (5 points)