To test H0: p = 0.75 versus H1: p 6 < 0.75, a simple random sample of

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To test H0: p = 0.75 versus H1: p 6 < 0.75, a simple random sample of n = 400 individuals is obtained and x = 280 successes are observed.

(a) What does it mean to make a Type II error for this test?

(b) If the researcher decides to test this hypothesis at the α = 0.01 level of significance, compute the probability of making a Type II error if the true population proportion is 0.71. What is the power of the test?

(c) Redo part (b) if the true population proportion is 0.68.

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