Researchers at the FDA are interested in the effectiveness of a generic pain-relieving drug compared to that of a brand-name drug on the basis of the length of time between drug administration and pain cessation. They plan to test the generic drug on 36 randomly selected subjects with pain symptoms. If the generic drug has significantly shorter length of time to pain cessation then researchers will recommend sale of the generic drug. The brand-name drug is known to relieve symptoms at 1.5 hours, on average, after administration of the drug with a population standard deviation of 0.25 hours. It is assumed that the time to cessation on the generic drug has the same standard deviation of the brand name drug. They intend to perform a two-sided hypothesis test at the 3% significance level. (a) What are the null and alternative hypotheses? Be sure to define the population parameter of interest. (b) Suppose that the data have been collected and the researchers found enough evidence to reject the null hypothesis given in part (a). What is the probability that they committed a Type II error?
Researchers at the FDA are interested in the effectiveness of a generic pain-relieving drug compared to that of a brand-name drug on the basis of the length of time between drug administration and pain cessation. They plan to test the generic drug on 36 randomly selected subjects with pain symptoms. If the generic drug has significantly shorter length of time to pain cessation then researchers will recommend sale of the generic drug. The brand-name drug is known to relieve symptoms at 1.5 hours, on average, after administration of the drug with a population standard deviation of 0.25 hours. It is assumed that the time to cessation on the generic drug has the same standard deviation of the brand name drug. They intend to perform a two-sided hypothesis test at the 3% significance level.
(a) What are the null and alternative hypotheses? Be sure to define the population parameter of interest.
(b) Suppose that the data have been collected and the researchers found enough evidence to reject the null hypothesis given in part (a). What is the probability that they committed a Type II error?
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