A box of dice contains one that has been altered by changing the side with one d

Question

A box of dice contains one that has been altered by changing the side with one dot (ace) to five dots. Thus, the altered die has no aces but two sides with five dots. A die is chosen at random and rolled 24 times. A fair die is expected to come up ace 4 times in 24 rolls. Consider the hypotheses
H0: It's a good die vs. Ha: It's the altered die.
Use the following decision rule: Reject H0 if an ace never comes up in the 24 rolls, and retain H0 otherwise.

(a) Specify the appropriate hypotheses in mathematical symbols.
(b) Find , the probability of a type I error.
(c) Find , the probability of a type II error.

Explanation / Answer

Ho: P(1)=.1666 Ha: P(1) doesn't = .1666 so again we need the binomial: (n choose k)*p^k*(1-p)^(n-k) b) a type 1 error would occur if we think it's a fake dice when it's real. So we need 24 non aces. (5/6)^24=0.0125791152 c) a type 2 error would occur if we think it's a real dice when it's fake. But that would never happen because it has no aces. So beta is 0.

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