please help wtih these

6.16 Is college worth it? Part I: Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school. The test statistic is: * (please round to two decimal places) The p-value associated with this hypothesis test is: * (please round to four decimal places) What is the conclusion of the hypothesis test? Since pra we reject the null hypothesis and accept the alternative Since p 2 a we reject the null hypothesis and accept the alternative O Since p 2 a we accept the null hypothesis Since p > a we do not have enough evidence to reject the null hypothesis O Since pea we fail to reject the null hypothesis5.32 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)\fGaming and distracted eating, Part I: A group ofresearchers are interested in tine possible e'ects ofdistracting stimuli during eating: such as an increase or decrease in the amount of food consumption. To test this hypothesis, they monitored food intake for a group of 44 patients who were randomized into two equal groups. The treatment group ate lunch While playing solitaire, and the control group ate lunch without any added distractions. Patients in the treatment group ate 52.1 grams ofbiscuits: with a standard deviation of 45.1 grams, and patients in the control group ate 2?.1 grams ofhiscuits= with a standard deviation of 25.4 grams. Do these data provide convincing evidence that the average food intake (measured in amount of biscuits consumed) is di'erent for the patients in the treatm- s oup? Assume that conditions for inference are satised. The test statistic for the hypothesis test is: :I: :ll nfease round to two decimaipfaces) The pvalue for the hypothesis test is: :8 {please round tofonr decimalplacer) Interpret the result of the hypothesis test in the context of the study: \f6.18 Is college worth it? Part II: Exercise 6.16 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot afford it. (a) Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context. lower bound: *(please round to four decimal places) upper bound: *(please round to four decimal places) Interpret the confidence interval in context: (b) Suppose we wanted the margin of error for the 90% confidence level to be about 1.5%. How large of a survey would you recommend? A survey should include at least *people.6.34 Prenatal vitamins and Autism: Researchers studying the link between prenatal vitamin use and autism sun-eyed the mothers of a random sample of children aged 24 60 months with autism and conducted another separate random sample for children with typical development. The table below shows the number of mothers in each group who did and did not use prenatal vitamins dining the three months before pregnancy (periconoeptional period). (Schmidt, 2011) ' :."*-. 'h'lJ-JMIM'I rs orma'Iaiu-.-_.._- _..- "43.1: more '_''-______ (b) Complete the hypothesis test and state an appropriate conclusion. What is the value of the test statistic for this test? |:|I (Please round :0 Mo decimal pieces) What is the pvalue associated Twith this test? :8 {Please round tofonr decimalptacerj The result of the hypothesis is: 6.36 Diabetes and unemployment: A 2012 Gallup poll surveyed Americans about their employment status and whether or not they have diabetes. The survey results indicate that 1.5% of the 47,774 employed (full or part time) and 2.5% of the 5,855 unemployed 18-29 year olds have diabetes. (a) Create a two-way table presenting the results of this study. Diabetes No Diabetes Employed Unemployed6.42 Evolution versus Creationism: A Gallup Poll released in December 2010 asked 1019 adults living in the Continental U_S_ about their belief in tile origin of humans. These results, along with results from a more comprehensive poll from 2001 (that we will assume to be exactly aocurate), are summarized in the table below: Year: 2010 1Fear: 2001 Humans Evolved with God guiding (1) Humans evolved but God had no part in the process (2) God created humans in present form (3) Other I' No opinion (4) V (b.-"c) Calculate the actual number of respondents in 2010I that fall in each response category as well as the expected number, assuming that the population follows the 2001 distribution. otsam media the nearest whole number} Observed 2010 Expected 2010 Response Humans Evolved with God guiding (l) Humans evolved but God had no part in the process (2) God created humans in present form (3) Other a\" No opinion (4) (d) Conduct a chi square test and state your conclusion The value of the test statistic is: :8 (please round to two decimalplaces} The degrees of 'eedorn for this test are: :l: The p~value for this test is: :I: [please round :ofonr decimalpiaces} State the conclusion of the test in the context of the problem: 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)