MAT 167: StatisticsFinal ExamInstructor: Anthony TanbakuchiSummer 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. Show your work in thespace provided. If you choose to use R, write what you typed on the test or copyand paste your work into a word document labeling the question number itcorresponds to. When you are done with the test print out the document and turnit in with the test. Be sure to save often on a memory stick just in case. Using anyother program or having any other documents open on the computer willconstitute 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 16 questions for a total of 80 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 80 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. one sample proportion test20. two sample proportion test21. test of homogeneity22. test of independence23. linear correlation coefficient & test24. regression25. 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) A researcher at the department of labor wants to determine if the proportion ofmen who work in sociology, psychology, and anthropology is the same from recent studydata on the subject.(b) (2 points) A math department committee wants to award $50 to the student who receivedthe best score on their calculus final exam this past semester. However, the three facultywho taught calculus last semester gave different final exams. What method could helpidentify the top student amongst the three different exams?(c) (2 points) A drug research would like to test the claim that the mean absorption of 1 gramof vitamin E is the same for four methods of delivery: topical, intravenous, oral, and nasalInstructor: Anthony Tanbakuchi Points earned: / 6 pointsMAT 167: Statistics, Final Exam p. 2 of 9spray.(d) (2 points) A researcher is using a statistical hypothesis test that requires the populationwhich the sample was drawn from to have a normal distribution. How could the researchercheck this assumption?(e) (2 points) A drug researcher wants to determine if a new growth hormone drug can increasethe mean weight of mice as compared to a control group of mice.2. (1 point) The test of homogeneity can be thought of as a generalization of what two sampletest?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. (2 points) Under what conditions can we approximate a binomial distribution as a normaldistribution?5. (2 points) Give a clear specific example of when you would use a population distribution.Instructor: Anthony Tanbakuchi Points earned: / 10 pointsMAT 167: Statistics, Final Exam p. 3 of 96. (2 points) Give a clear specific example example of when you would use a sampling distri-bution.7. (1 point) What percent of data lies within one standard deviation as stated by the EmpiricalRule?8. The following questions regard hypothesis testing in general.(a) (1 point) 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?(b) (1 point) Do we use the population distribution or the sampling distribution when calcu-lating the p-value?(c) (1 point) If you fail to reject H0but H0is false. What type of error has occurred? (TypeI or Type II)(d) (1 point) What variable represents the actual Type I error?(e) (1 point) What variable is used to represent a Type II error?(f) (1 point) What does the power of a hypothesis test represent?(g) (1 point) In the one sample mean test with σ unknown, what is the distribution of thetest statistic?(h) (2 points) Why is it important to use random sampling?9. A consumer advocate group believes that Crystal Springs Sparkling Mineral Water containsmore than the advertised 35 mg of sodium per serving. They randomly sample 40 servingsInstructor: Anthony Tanbakuchi Points earned: / 12 pointsMAT 167: Statistics, Final Exam p. 4 of 9and measure the amount of sodium contained in each sample. The collected data has a samplemean of 37.5 mg, and a sample standard deviation of 8.2 mg.(a) (2 points) What is the null and alternative hypothesis?(b) (1 point) What hypothesis test should be used?(c) (2 points) What are the requirements for the hypothesis test? Are they met?(d) (1 point) What significance level will you use?(e) (2 points) Manually compute the p-value.(f) (1 point) What is the formal decision?(g) (2 points) What is the final conclusion?10. A craps table at a local casino has been losing more money than normal. It seems that betsinvolving a one on the face of the dice (such as “snake eyes”) are appearing more than usual.The casino manager thinks that the dice have been weighted to cause the side with one to havea higher probability of occurring than a fair dice.(a) (2 points) The casino manager takes one of the dice from the table and flips it 100 times,the side with a value of one appears 26 times. Construct a 95% confidence interval for theInstructor: Anthony Tanbakuchi Points earned: / 13 pointsMAT 167: Statistics, Final Exam p. 5 of 9true probability of getting a one with this die.(b) (1 point) If