A psychologist is studying smokers' self-images, which she measures using the self-image (SI) score from a personality inventory. She would like to examine themeanSI score for thepopulationof all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is82 and that thestandard deviationis12, but the psychologist believes that the value for the mean has increased. She decides to perform astatistical testand chooses arandom sampleof 100 smokers' SI scores. She'll use the value12 for the population standard deviation, and she'll test at the0.01 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated.

A. What are the null and alternative hypotheses that the psychologist should use for the test? H0 : is?

less than, less than or equal to, greater than, greater than or equal to, not equal to, equal to?

82, 100, 85, 12

H1 : is less than, less than or equal to, greater than, greater than or equal to, not equal to, equal to?

82, 100, 85, 12

B. Assuming that the actual value of is 85, what is thepowerof the test? Round your response to at least two decimal places.

C. What is the probability that the psychologist rejects the null hypothesis when, in fact, it is true? Round your response to at least two decimal places.

D. Suppose that the psychologist decides to perform another statistical test using the same population, the same null and alternative hypotheses, and the same level of significance, but for this second test the psychologist chooses a random sample of size 150 instead of a random sample of size 100. Assuming that the actual value of is 85, how does the probability that the psychologist commits a Type II error in this second test compare to the probability that the psychologist commits a Type II error in the original test?

The probability of committing a Type II error in the second test is greater?

The probability of committing a Type II error in the second test is less?

The probabilities of committing a Type II error are equal?

I really can't get the hang of solving B.