To test H_0: p = 070 versus H_1: p > 0.70, a simple random sample of n = 500 ind

Question

To test H_0: p = 070 versus H_1: p > 0.70, a simple random sample of n = 500 individuals is obtained and x = 69 successes are observed. (a) What does it mean to make a Type II error for this test? (b) f the researcher decides to test this hypothesis at the alpha = 0.01 level of significance, compute the probability of making a Type II error beta if the true population proportion is 0.76 What (a) What does it mean to make a Type Il error for this test? Choose the correct answer below. A. H_0 is not rejected and the true population proportion is equal to 0.70. B. H_0 is not rejected and the true population proportion is greater than 0. 70 C. H_0 is rejected and the true population proportion is less than 0.70. D. H_0 is rejected and the true population proportion is greater than 0.70 (b) If the researcher decides to test this hypothesis at the alpha = 0.01 level of significance compute the probability of making a Type II error beta if the true population proportion is 076 What is (Type integers or decimals rounded to four decimal places as needed).

Explanation / Answer

Answer:

a).

B. Ho is not rejected when population proportion is > 70.

b).

MINITAB used

Power and Sample Size

Test for One Proportion

Testing p = 0.7 (versus > 0.7)

= 0.01

              Sample

Comparison p    Size     Power

        0.76     500 0.740617

=0.2594

Power= 0.7406

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