3. A random sample of size 64, from a population with variance 02 = 256 is to be used to test the null hypothesis that for a certain age group the mean score on an achievement test is less than or equal to 40.0 against the alternative that it is greater than 40.0. If the null hypothesis is to be rejected if and only if the mean of the random sample exceeds 43.5, nd (a) the probabilities of type I error when a = 37, 38, 39, and 40; (b) the probabilities of type II errors when u = 41, 42, 43, 44, 45, 46, 47, and 48. Also plot the power function. For (a) and (b), feel free to use any software to do the calculation and please summarize your results in a table like the one below (some of the entries in the table will be empty): 6 P(type I error)=a(6) P(type II error)=(9) p0wer(6) l