Stats 250 F16 Final Exam Solutions Page 8 of 10 7.Vitamin C and the Common Cold: Wisconsin’s Department of Public Health has extensively studied winter colds. With the daily use of vitamin C, the probability a Wisconsin resident survives a winter season without a cold is 0.63. As part of a study, 90 Wisconsin residents who take vitamin C daily will be chosen at random. Let Xbe the number in the sample who survive the winter season without a cold. a. Suppose 50 of the selected residents survived the winter season without a cold. How many standard deviations does this observed value of 50 fall belowthe mean?  Final answer: _______ _________ b. If the true survival rate is indeed 63%, how likely would it be to observe only 50 or fewer of the sampled vitamin C using residents survive the winter season without a cold?  Final answer: _______ _________ c.If a researcher were using the study results to test the theory that the true rate of surviving a winter without a cold is less than the stated 63%, what is the statistical name for the probability in part (b)? 
8.So many places to eat!According to research by a community health department, eating takeout or fast food may actually be better for your body than dinner at a full service restaurant. The researchers decided to learn more about how the number of fast food restaurants compares to the number of full service restaurants for all counties in Michigan. They took a random sample of Michigan counties and the 99% confidence interval for the mean difference in the number of restaurants for Michigan counties (fast food minus full service) was calculated to be (-0.6 restaurants, 8.6 restaurants). The corresponding 95% confidence interval on the same set of data was calculated to be (0.2 restaurants, 7.8 restaurants). a.Which of the following could be a possible p-value for the hypotheses: H0͗ ʅd= 0 vs. Ha͗ ʅdт Ϭ͍ Circle all that apply. b.For each statement below, determine if it is a correct or incorrect statement. Clearly circle your answer.  One of the assumptions we must check is that the population mean difference in the number of restaurants for all Michigan counties (fast food minus full service) follows a normal distribution.