Predicting Election Results Throughout the US presidential election of 2012, polls gave regular updates on the sample proportion supporting each candidate and the margin of error for the estimates. This attempt to predict the outcome of an election is a common use of polls. In each case below, the proportion of voters who intend to vote for each candidate is given as well as a margin of error for the estimates. Indicate whether we can be relatively confident that candidate A would win if the election were held at the time of the poll. (Assume the candidate that gets more than 50%'of vote wins). 1. Candidate A: 54% & Candidate B:46% with Margin of error: + 5% 2. Candidate A: 52% & Candidate B:48% with Margin of error: + 1% 3. Candidate A: 53% & Candidate B:47% with Margin of error: + 2% 4. Candidate A: 58% & Candidate B:42% with Margin of error: + 10% In Exercises 1,2 and 3 state the null and alternative hypotheses for the statistical test described. 1. Testing to see if there is evidence that the mean of group A is not the same as the mean of group B 2. Testing to see if there is evidence that a mean is less than 50 3. Testing to see if there is evidence that the pro- portion of people who smoke is greater for males than for females QUESTION 4 Multiple Sclerosis and Sunlight It is believed that sunlight offers some protection against multiple sclerosis (MS) since the disease is rare near the equator and more prevalent at high latitudes. What is it about sunlight that offers this protection? To find out, researchers15 injected mice with proteins that induce a condition in mice comparable to MS in humans. The control mice got only the injection, while a second group of mice were exposed to UV light before and after the injection, and a third group of mice received vitamin D supplements before and after the injection. In the test comparing UV light to the control group, evidence was found that the mice exposed to UV suppressed the MS-like disease significantly better than the control mice. In the test comparing mice getting vitamin D supplements to the control group, the mice given the vitamin D did not fare significantly better than the control group. If the p-values for the two tests are 0.472 and 0.002, which p-value goes with which test? UV: Vitamin D: