Power For a hypothesis test with a specified significance level α, the probability of a type I error is a, whereas the probability β of a type II error depends on the particular value of p that is used as an alternative to the null hypothesis. a. Using an alternative hypothesis of p < 0.4, a sample size of n = 50, and assuming that the true value of p is 0.25, find the power of the test. See Exercise 1 in Section 8-2. ( Hint: Use the values p = 0.25 and  pq/n = (0.25)(0.75)/50.) b. Find the value of ß, the probability of making a type II error. c. Given the conditions cited in part (a), what do the results indicate about the effectiveness of the hypothesis test? Exercise 1  Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.

Question

Power For a hypothesis test with a specified significance level α, the probability of a type I error is a, whereas the probability β of a type II error depends on the particular value of p that is used as an alternative to the null hypothesis.

a. Using an alternative hypothesis of p < 0.4, a sample size of n = 50, and assuming that the true value of p is 0.25, find the power of the test. See Exercise 1 in Section 8-2. ( Hint: Use the values p = 0.25 and  pq/n = (0.25)(0.75)/50.)

b. Find the value of ß, the probability of making a type II error.

c. Given the conditions cited in part (a), what do the results indicate about the effectiveness of the hypothesis test?

Exercise 1 

Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.

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