# Question

A study is designed to test H0: p = 0.50 against Ha: p > 0.50, taking a random sample of size n = 100, using significance level 0.05.

a. Show that the rejection region consists of values of p̂ 7 0.582.

b. Sketch a single picture that shows (i) the sampling distribution of p̂ when H0 is true and (ii) the sampling distribution of p̂ when p = 0.60. Label each sampling distribution with its mean and standard error, and highlight the rejection region.

c. Find P(Type II error) when p = 0.60.

a. Show that the rejection region consists of values of p̂ 7 0.582.

b. Sketch a single picture that shows (i) the sampling distribution of p̂ when H0 is true and (ii) the sampling distribution of p̂ when p = 0.60. Label each sampling distribution with its mean and standard error, and highlight the rejection region.

c. Find P(Type II error) when p = 0.60.

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