To test H0 p 0 45 versus H1 p 0 45, a simple random sample of n 500 individuals is obtained and x 245 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 0 1 level of significance, compute the probability of making a Type II error if the true population proportion is 0 49 What is the power of the test (c) Redo part (b) if the true population proportion is 0 47

Question: To test H0: p = 0.45 versus H1: p 0.45, a simple random sample of n = 500 individuals is obtained and x =

To test H0: p = 0.45 versus H1: p ≠ 0.45, a simple random sample of n = 500 individuals is obtained and x = 245 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 = 0.1 level of significance, compute
the probability of making a Type II error if the true population proportion is
0.49. What is the power of the test?
(c) Redo part (b) if the true population proportion is 0.47.

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