Question

Toss the coin four times. If the coin lands either all heads or all tails, reject...

Toss the coin four times. If the coin lands either all heads or all tails, reject H0: p=1/2. (The p denotes the chance for the coin to land on heads.) Complete parts a and b.

(a) What is the probability of a Type I error for this procedure?

(b) If p = 4/5, what is the probability of a Type II error for this procedure?

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Answer #1

a) The probability of type I error is computed as the probability of rejecting the null hypothesis when it is True. Therefore, here it would be defined as the probability of getting all heads or all tails when p = 0.5 is the real probability of getting a heads. Therefore the type I error probability is computed here as:

Therefore 0.125 is the required probability here.

b) Given that the true probability of getting heads is 4/5 = 0.8, the probability of type II error is computed here as:
= 1 - Probability that all were heads - Probability that all were tails

Therefore 368/625 is the required probability of type II error here.

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