- me world renown supplier of delicious food is looking to direct more of its advertising budget towards women. Before they do this, they hire a consulting rm to compare the proportion of men and women who are the primary grocery shoppers in their household. Denoting the population proportions by P"1 and PW, a two-proportion z-test is carried out to test Ho: Pm = Pw against Ha: Pw > Pm- The value of the test statistic is found to be 2 = 0.124, and the p-value for the test is found to be 0.183. a) Is this a one tailed test or a two tailed test? Why was this type of test chosen? b) Should the consulting rm pool the variances for this z-test? Why or why not? c) interpret p in context. d) What does 2 = 0.124 tell you? 2. Gastric freezing was once a recommended treatment for ulcers in the upper intestine. This process involved putting the patient under anesthesia, putting a balloon down into their stomach, and lling the balloon with freezing coolant. For years this treatment was considered effective against stomach ulcers, until a health insurance company decided to conduct a clinical trial. For this clinical trial, 170 patients with ulcers were randomly divided into two. 40 of the 87 patients who received the freezing treatment showed improvement, while 39 of the 83 patients that received a placebo improved. Does this study provide evidence that gastric freezing is more effective in treating ulcers than a placebo? 3. In the country of Wardlonia, a vaccine is approved if it can be shown to be at least 85% effective, meaning that it prevents disease in 85% of the people who take it. Staubco Pharmaceuticals just developed a new and exciting drug known as Staubavox and they are claiming it should be approved. Their Chief Research Scientist, Dr. B. Davies Staubatron, is going to conduct a quick study to prove it that the efcacy is 85% or greater. Assume the requirements for an effective study are met. a. if he tests 100 people, how many people does the vaccine have to work on in order to conclud that his vaccine is at least 85% effective. Assume he is a bad medical director and only wants an alpha level = 10%. Make sure you show all your work, including where every number came from and a sketch of the Normal curve showing the relevant area shaded in. b. Assume that after when conducting his z-test, he obtains a p-value of 0.06 and rejects the null if he shouldn't have rejected the null, i. Which error did he make Type I or Type II? ii. Describe this error in context. iii. What is the consequence of this error? iv. What is the probability of making this type of error under these conditions