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5.32 Fuel efficiency of manual and automatic cars, Part I: Each year the US Environmental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. Below are summary statistics on fuel efficiency (in miles/ gallon) from random samples of cars with manual and automatic transmissions manufactured in 2012. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? Assume that conditions for inference are satisfied. City MPG, Automatic City MPG, Manual Mean 16.12 19.85 SD 3.58 4.51 n 26 26 357 25 - 15 J automatic manual City MPG Miual The test statistic is:[ * (please round to two decimal places) The p-value is: * (please round to four decimal places)5.6 Fuel efficiency of Prius: Fueleconomy.gov, the official US government source for fuel economy information. allows users to share gas mileage information on their vehicles. The histogram below shows the distribution of gas mileage in miles per gallon (MPC) from 14 users who drive a 2012 Toyota Prius. The sample mean is $3.3 MPG and the standard deviation is 5.3 MPCi. Note that these data are user estimates and since the source data cannot be verified, the accuracy of these estimates are not guaranteed. 6 4 2 40 45 50 55 60 65 Mileage (in MPG) st we should use a: There are degrees of freedom for this test. The best statistic is it (please moaned to te decimal place) The p-value for this hypothesis nest is: (please round to four decimal places) I'be conclusion for the hypothesis lest is: Q Since p2 a we reject the null hypothesis and accept the alternative Since per we fail to reject the null hypothesis Since pa a we accept the null hypothesis O Since pea we reject the wall hypothesis and accept the alternative O Since p 2 a we do not have enough evidence to reject the null hypothesis (c) Calculate a 93%% confidence interval for the average gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov. We are confident that the true population gas mileage of a 2012 Prius by drivers who participate on feeleconomy.gov is between ming and Impg (please round to one decimal place)SAT scores of students at an Ivy League college are distributed with a standard deviation of 250 points. Two statistics students, Raina and Luke, want to estimate the average SAT score of students at this college as part of a class project. They want their margin of error to be no more than 25 points. (a) Raina wants to use a 90% confidence interval. How large a sample should she collect? Raina should sample at least * people. wants - that oft thanctusl sandely size. moremenme whether his the level baconbacks (c) Calculate the minimum required sample size for Luke. Luke should sample at least *people.Question with last attempt is displayed for your review only We considered the differences between the temperature readings in January 1 of 1968 and 2008 at 51 locations in the continental US in Exercise 5.19. The mean and standard deviation of the reported differences are 1.1 degrees and 4.9 degrees respectively. (a) Calculate a 90% confidence interval for the average difference between the temperature measurements between 1968 and 2008. lower bound: degrees(please round to two decimal places) upper bound: degrees (please round to two decimal places)We considered the differences between the reading and writing scores of a random sample of 200 students who took the High School and Beyond Survey. The mean and standard deviation of the differences are Xread-write = -0.545 and 8.887 points respectively. (a) Calculate a 95% confidence interval for the average difference between the reading and writing scores of all students. lower bound: points (please round to two decimal places) upper bound: points (please round to two decimal places)