A bowl contains 2 red balls, 2 white balls, and 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 4 balls at random from the bowl, one at a time and WITH replacement. Let X equal the number of red balls drawn.

Define the critical region C for this test is terms of X.

For the critical region C, find the values of $\displaystyle \alpha$ and $\displaystyle \beta$.

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