A bowl contains two red balls, two white balls, and a fifth ball that is either red or white. Let p denote the probability of drawing a red ball from the bowl. We shall test the simple null hypothesis H0: p = 3/5 against the simple alternative hypothesis H1: p = 2/5. Draw four balls at random from the bowl, one at a time and with replacement. Let X equal the number of red balls drawn.
(a) Define a critical region C for this test in terms of X.
(b) For the critical region C defined in part (a), find the values of α and β.