Question

A hypothesis test will be performed to test the claim that a population proportion is less than 0.70. A sample size of 400 and significance level of 0.025 will be used. If p = 0.62, find the probability of making a type II error, β.

1. Answer:
2. A. Fill in the blanks below to describe the sampling distribution of ??� assuming H₀ is true.

Mean:

Standard deviation:

Shape:

             Sketch the sampling distribution of ??� assuming H₀ is true.

1. B. Specify the rejection region when ??� is used as the test statistic. Locate the rejection region on your graph from part a.
2. C. Describe the sampling distribution of ??� if p = .62.

Mean:

Standard deviation:

Shape:

       On your graph from part a, sketch the sampling distribution of ??� if p =.62.

1. D. Find the probability of failing to reject H₀ if p is actually equal to .62. That is, find the probability of making a Type II error if p = .62. Shade the area corresponding to this probability on your graph.

Answer 1

B.