Let X1, X2, ... , Xn denote a random sample from a normal population distribution with a known value of sigma. For testing the hypotheses HO: mean = mean0 versus Ha: mean > mean0 where mean0 is a...

Let X1, X2, ... , Xn denote a random sample from a normal population distribution

with a known value of sigma. For testing the hypotheses HO: mean = mean0 versus Ha: mean > mean0 where mean0 is a fixed number, the test procedure consists of test statistics X(bar) and rejection region x(bar)>102.33. Assume mean0 = 100, n = 25, and sigma = 5.

a) What is the probability of committing a type 1 error when mean = 99?

b) What is the probability of committing a type 1 error when mean = 98?

c) In general, what can be said about the probability of a type 1 error when the actual mean value is below the mean0 value?