MAT 167: StatisticsFinal ExamInstructor: Anthony TanbakuchiSpring 2008Name:Computer / Seat Number:No books, notes, or friends. Show your work. You may use the attachedequation sheet, R, and a calculator. No other materials. If you choose to use R,write what you typed on the test or copy and paste your work into a worddocument labeling the question number it corresponds to. When you are donewith the test print out the document. Be sure to save often on a memory stick justin case. Using any other program or having any other documents open on thecomputer will constitute cheating.You have until the end of class to finish the exam, manage your time wisely.If something is unclear quietly come up and ask me.If the question is legitimate I will inform the whole class.Express all final answers to 3 significant digits. Probabilities should be given as adecimal number unless a percent is requested. Circle final answers, ambiguous ormultiple answers will not be accepted. Show steps where appropriate.The exam consists of 12 questions for a total of 70 points on 9 pages.This Exam is being given under the guidelines of our institution’sCode of Academic Ethics. You are expected to respect those guidelines.Points Earned: out of 70 total pointsExam Score:MAT 167: Statistics, Final Exam p. 1 of 91. The following is a partial list of statistical methods that we have discussed:1. mean2. median3. mode4. standard deviation5. z-score6. percentile7. coefficient of variation8. scatter plot9. histogram10. pareto chart11. box plot12. normal-quantile plot13. confidence interval for a mean14. confidence interval for difference in means15. confidence interval for a proportion16. confidence interval for difference in pro-portions17. one sample mean test18. two independent sample mean test19. match pair test20. one sample proportion test21. two sample proportion test22. test of homogeneity23. test of independence24. linear correlation coefficient & test25. regression26. 1-way ANOVAFor each situation below, which method is most applicable?• If it’s a hypothesis test, also state what the null and alternative hypothesis are.• If it’s a graphical method, also describe what you would be looking for.• If it’s a statistic, how susceptible to outliers is it?(a) (2 points) Ten pairs of chicks were selected to test the effect of a vitamin supplement onearly growth. The chicks in each pair were siblings of high birth weight. One chick ineach pair was given the supplement and the other was not. After two weeks, the weightof each chick was recorded. The researcher would like to test the research hypothesis thatthe supplement increases the growth rate of chicks in the first weeks after hatching againstthe null hypothesis that it has no effect.(b) (2 points) A researcher would like to compare the distribution of incomes of individualsin the four major regions of the US: the west, the south, the midwest, the east.(c) (2 points) A researcher wants determine if the mean income in the four major regions ofInstructor: Anthony Tanbakuchi Points earned: / 6 pointsMAT 167: Statistics, Final Exam p. 2 of 9the US — the west, the south, the midwest, the east — are not all the same.(d) (2 points) An investigator is interested in the success of a job training program for currentwelfare recipients. If fewer than 30% of participants in the program are able to find workwithin three months, the program will be discontinued.(e) (2 points) A high school principal is interested in how well she can predict the number ofdays that her students miss school as a function of their GPA.(f) (2 points) A manufacturer needs to measure how consistently a new machine can cut nailsto the desired length.2. (1 point) 1-Way ANOVA can be thought of as a generalization of what two sample test?3. (1 point) If the mean, median, and mode for a data set are all the same, what can you concludeabout the data’s distribution?4. The following questions regard hypothesis testing in general.(a) (2 points) When we conduct a hypothesis test, we assume something is true and calculatethe probability of observing the sample data under this assumption. What do we assumeis true?Instructor: Anthony Tanbakuchi Points earned: / 10 pointsMAT 167: Statistics, Final Exam p. 3 of 9(b) (2 points) Do we use the population distribution or the sampling distribution when cal-culating the p-value?(c) (2 points) If you reject H0but Hais false. What type of error has occurred? (Type I orType II)(d) (2 points) In the one sample proportion test, what is the distribution of the test statistic?(e) (2 points) In the one sample proportion test, what requirements must be met so that thetest statistic’s distribution is valid?(f) (2 points) Why is it important to use random sampling?(g) (2 points) A two sample mean hypothesis test was conducted with H0: ∆µ = 0 andHa: ∆µ > 0. The first and second samples had respective sample sizes of 18 and 20. Thetest statistic calculated from the sample data is t = 1.89. Find the p-value.5. Nine students were randomly selected who had taken the SAT twice. A researcher would liketo test the claim that students who take the SAT test a second time score higher than theirfirst test.Student A B C D E F G H IFirst SAT Score 480 510 530 540 550 560 600 620 660Second SAT Score 460 500 530 520 580 580 560 640 690(a) (1 point) What type of hypothesis test will you use?(b) (2 points) What are the test’s requirements?Instructor: Anthony Tanbakuchi Points earned: / 15 pointsMAT 167: Statistics, Final Exam p. 4 of 9(c) (2 points) What are the hypothesis H0and Ha?(d) (1 point) What α will you use?(e) (2 points) Conduct the hypothesis test. What is the p-value?(f) (1 point) What is your formal decision?(g) (2 points) State your final conclusion in words.6. The following table lists the the fuel consumption (in miles/gallon) and weight (in lbs) of avehicle.Weight3175 3450 3225 3985 2440 2500 2290MPG 27 29 27 24 37 34 37(a) (2 points) Upon looking at the scatter plot of the data, the relationship of fuel consumptionand milage looks linear. Is the linear relationship statistically significant? (Justify youranswer with an analysis.)(b) (2 points) What percent of a vehicle’s fuel consumption can be explained by its weight?(c) (2 points) You are designing a new vehicle and would like to be able to predict its fuelconsumption. Write the equation for fitted model (with the actual values of the coeffi-Instructor: Anthony Tanbakuchi Points earned: / 14