For each of the following questions, a) Write the claim mathematically. Identify H. and Ha. b) Find the critical value(s) and identify the rejection region(s). c) Calculate the appropriate test statistic. d) Decide whether to reject or fail to reject the null hypothesis, then interpret this decision in the context of the original claim.2) The Western blot assay is a blood test for the presence of HIV. It has been found that the 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 blood donors who do not have HIV found that 3 received a false positive test result. Test the researcher's claim of a 2% false positive rate at the alpha = 0.05 level. What can you conclude? Z = Vee 3. A citrus grower's association believes that the mean utilization of fresh citrus fruits by people in the United States is at least 22 pounds per year. A random sample of 103 people in the United States has a mean utilization of fresh citrus fruits of 21.6 pounds per year and a standard deviation of 7 pounds. At a = 0.02, can you reject the association's claim that the mean utilization of fresh citrus fruits by people in the United States is at least 22 pounds per year? (Adapted from U.S. Department of Agriculture)4. An auto maker estimates that the mean gas mileage of its sports utility vehicle is at least 20 miles per gallon. A random sample of 8 such vehicles had a mean of 18 miles per gallon and a standard deviation of 5 miles per gallon. At a = 0.05, can you reject the auto maker's claim that the mean gas mileage of its sports utility vehicle is at least 20 miles per gallon? Assume the population is normally distributed. (Adapted from Consumer Reports)population is normally distributed, A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use. In a random sample of 57 microwaves that are 5 years old, 13% needed repairs. At a = 0.04, can you reject the maker's claim that no more than 10% of its microwaves need repair during the first five years of use? (Adapted from Consumer Reports)A state school administrator says that the standard deviation of SAT critical reading test scores is 113. A random sample of 14 SAT critical reading test scores has a standard deviation of 108. At a = 0.01, test the administrator's claim. What can you conclude? Assume the population is normally distributed. (Adapted from College Board Online)