# Question

Consider Example 13 about testing H0: p = 1/3 against Ha: p > 1/3 for the astrology study, with n = 116. Find P(Type II error) for testing H0: p = 1/3 against Ha: p > 1/3 when actually p = 0.50, if the sample size is 60 instead of 116. Do this by showing that

a. The standard error is 0.061 when H0 is true.

b. The rejection region consists of p̂ values above 0.433.

c. When p = 0.50, the probability that p̂ falls below 0.433 is the left-tail probability below -1.03 under a standard normal curve. What is the answer? Why would you expect P(Type II error) to be larger when n is smaller?

a. The standard error is 0.061 when H0 is true.

b. The rejection region consists of p̂ values above 0.433.

c. When p = 0.50, the probability that p̂ falls below 0.433 is the left-tail probability below -1.03 under a standard normal curve. What is the answer? Why would you expect P(Type II error) to be larger when n is smaller?

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