take a 10 point multiple choice test over the material. Their scores follow:GroupTest ScoresConstant sound74686629Random sound55344722No sound2471215511

Conduct an F-test and prepare ANOVA Table.Interpret the results and commentabout the Hypothesis.4. Use the data below, showing a summary of highway gas mileage for several obser-vations, to decide if the average highway gas mileage is the same for mid-size cars,SUV’s, and pick-up trucks. Test the appropriate hypotheses at theα= 0.01 level.nMeanStd. Dev.Mid-size3125.82.56SUV’s3122.683.67Pick-ups1421.292.765. A psychologist was interested in whether different TV shows lead to a more positiveoutlook on life. People were split into 4 groups and then taken to a room to view aprogram. The four groups saw: The Muppet Show, Futurama, The News, No program.After the program a blood sample was taken and serotonin levels measured (remembermore serotonin means more happy!The Muppet ShowBBC NewsFuturamaNo Program11447783786251411241193310864544Mean9.437.673.334.75Variance8.955.872.272.21Grand Mean6.30Grand Variance10.06(a) Carry out a one-way ANOVA by hand to test the hypothesis that some TV showsmake people happier than others.(b) Can you suggest some follow-up comparisons (with weights)?6. It is assumed that achievement test scores should be correlated with student’s class-room performance. One would expect that students who consistently perform well inthe classroom (tests, quizzes, etc.) would also perform well on a standardized achieve-ment test (0 - 100 with 100 indicating high achievement). A teacher decides to examinethis hypothesis. At the end of the academic year, she computes a correlation betweenthe students achievement test scores (she purposefully did not look at this data untilafter she submitted students grades) and the overall g.p.a. for each student computedover the entire year. The data for her class are provided below.Achvmnt.98969488917786715963GPA3.62.73.14.03.23.03.82.63.02.2Achvmnt.84797572868571939062GPA1.73.12.62.92.43.42.83.73.21.612

(a) Compute the correlation coefficient.(b) What does this statistic mean concerning the relationship between achievementtest performance and g.p.a.?(c) What percent of the variability is accounted for by the relationship between thetwo variables and what does this statistic mean?(d) What would be the slope and y-intercept for a regression line based on this data?(e) If a student scored a 93 on the achievement test, what would be their predictedG.P.A.? If they scored a 74? A 88?7. A statistics instructor at a large western university would like to examine the relation-ship (if any) between the number of optional homework problems students do duringthe semester and their final course grade. She randomly selects 12 students for studyand asks them to keep track of the number of these problems completed during thecourse of the semester. At the end of the class each student’s total is recorded alongwith their final grade. The data follows.ProblemsCourseGradePrb*Grd516231625868394462664092656642906867455676725472777356217872561678786084847361328576646091756825(a) For this setting, identify the response variable and the predictor variable.

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