8. During September 2018, United Airlines introduced a new two-line boarding process intended to decrease gate congestion, passenger anxiety, and time to board the plane. Independent random samples of similar cross-country ights for United Airlines and American Airlines were obtained and the boarding time (in minutes) for each was recorded. Assume both populations are normally distributed and the population standard deviations are unequal. Sample Size Sample Mean Sample Standard Deviation a) Find a 99% condence interval for the difference in boarding time between the two airlines. b) Does the condence interval produced in part a suggest at the 1% level that the mean boarding time is different for the two airlines? How do you know? 9. Research suggests that half of the American public believes in at least one conspiracy theory. Some of the more popular theories involve a secret group controlling the world, a faked moon landing, and Area 51 and aliens. The research results are often very different according to political affiliation. A random sample of Democrats and Republicans were asked if they believe pharmaceutical companies invent new diseases to make money. The resulting data are given in the table below. Political Affiliation Sample Size Number who believe pharmaceutical companies invent diseases Democrats 778 162 Republicans 750 149 a) Construct a 98% confidence interval for the difference in the proportion of voters who believe pharmaceutical companies invent diseases between the two political affiliations. b) Conduct a hypothesis test at the 0.02 level to test if there is evidence that the proportion of voters who believe pharmaceutical companies invent diseases is different between Democrats and Republicans. Does your conclusion agree with part a? c) Describe a Type I Error and Type II error here.10. A tine test is commonly used to determine whether a person has been exposed to tuberculosis. Approximately 2% of people in the United States have been exposed to tuberculosis. When the tine test is administered, 97% of people who have been exposed test positive, and 93% of those not exposed test negative. Suppose a person is randomly selected and given the tine test. Suppose the test is negative. What is the probability that the person actually has been exposed to tuberculosis? 11. A survey by YouGov showed that 33% of Americans believe that alien life has already contacted us but the US government has kept this information secret. Suppose ve Americans are selected at random. a) How many would you expect to believe alien life has already contacted us but the US government has kept this information secret (even if this value is not an integer)? b) What is the probability that in the random sample of ve Americans exactly two believe alien life has already contacted us but the US government has kept this information secret? c) What is the probability that in the random sample of ve Americans at least three believe alien life has already contacted us but the US government has kept this formation secret