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A researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOs) of major corporations. He has good reason to believe that the mean systolic blood pressure, u, of CEOs of major corporations is more than 132 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test and measures the systolic blood pressures of a random sample of 125 CEOs of major corporations. Suppose that the population of systolic blood pressures among CEOs of major corporations has a standard deviation of 15 mm Hg and that the researcher performs his hypothesis test using the 0.01 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) (a) What are the null hypothesis H, and the alternative hypothesis H, that the O P researcher should use for the test? S H , : (b) Assuming that the actual value of u is 136 mm Hg, what is the probability that the 0=0 030 020 researcher commits a Type II error? Round your response to two or more decimal places. X (c) What is the probability that the researcher rejects the null hypothesis when, in(c) What is the probability that the researcher rejects the null hypothesis when, in fact, it is true? Round your response to two or more decimal places. (d) Suppose that the researcher 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 researcher chooses a random sample of size 50 instead of a random sample of size 125. Assuming that the actual value of H is 136 mm Hg, how does the power of this second test compare to the power of the original test? The power of the second test is greater than the power of the original test The power of the second test is less than the power of the original test The powers of the two tests are equal