4. A majority of Suwon residents have favored increased fuel efficiency for automobiles. Some do not, primarily because of concern over increased cost, or from general opposition to government mandates. The public's intensity about the issue tends to fluctuate with the price of gasoline. In the summer of 2008, when the national average of prices for regular unleaded gasoline exceeded 2,000 Korean won per liter, fuel efficiency became part of the political landscape. How much the public does favor increased fuel efficiency has been the subject of numerous polls. A Gallup telephone poll of 1012 adults in March of 2009 reported that 810 favored the setting of higher fuel-efficiency standards for automobiles. Let p denote the probability that an adult does favor efficiency. Find 95% confidence interval for p. (5-point) 2 5. Recall the example of engine additives. 12 randomly chosen average mileage with additives from Boston to LA are reported as follows; ( 25.133, 25.259, 25.200, 24.602, 25.866, 25.653, 24.587, 25.623, 25.198, 24.945, 24.550, 24.758), Suppose these samples of size 12 are drawn from a normal distribution with =25.0 mpg and unknown standard deviation. a. State the null and the alternative hypotheses. (2-point.) b. Calculate the test statistic for . (3-point.) c. Test the null hypothesis at the 5% significance level and report your test result. (5-point) 6. A fair coin is tossed two hundred times. Let X = 1 if the ith toss comes up 200 heads and X, = 0 otherwise, i = 1,2,..., 200; X = X, Calculate the central i=1 limit theorem approximation for P(|X-E(X)|5). (5-point)