In Exercises 45 and 46,
(a) identify the claim and state H0 and Ha,
(b) find the critical value(s) and identify the rejection region(s),
(c) find the standardized test statistic z,
(d) decide whether to reject or fail to reject the null hypothesis, and
(e) interpret the decision in the context of the original claim. If convenient, use technology.
45. A polling agency reports that over 60% of U.S. adults think that the federal government’s bank bailouts were bad for the United States. In a random sample of 298 U.S. adults, 167 said that the federal government’s bank bailouts were bad for the United States. At a = 0.01, is there enough evidence to support the agency’s claim? (Adapted from Rasmussen Reports)
46. The Western blot assay is a blood test for the presence of HIV. It has been found that this test sometimes gives false positive results for HIV. A medical researcher claims that the rate of false positives is 2%. A recent study of 300 randomly selected U.S. blood donors who do not have HIV found that 3 received a false positive test result. At a = 0.05, is there enough evidence to reject the researcher’s claim? (Adapted from Centers for Disease Control and Prevention)