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UA MATH 167 - Study Notes

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MAT 167: StatisticsFinal ExamInstructor: Anthony TanbakuchiSpring 2009Name: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. Using any other program or having any otherdocuments open on the computer 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 24 questions for a total of 71 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 71 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?(a) (1 point) A researcher would like to estimate the mean weight of javalina.(b) (1 point) A researcher wants to determine if bear weights are normally distributed.(c) (1 point) An education researcher wants to determine if the probability a student willgraduate from middle school is effected by their economic status (poor, lower middle class,middle class, . . . ).(d) (1 point) A farmer wants to determine if the mean crop yield is the same for eight differentbrands of fertilizer.(e) (1 point) A fertility researcher wants to determine if a new drug can decrease the pro-portion of infertile mice. Twenty mice are randomly divided into two groups, a treatmentgroup and a control group.2. (1 point) What test is a many sample generalization of the two sample t-test?3. (1 point) If the mean, median, and mode for a data set are different, what can you concludeabout the data’s distribution?Instructor: Anthony Tanbakuchi Points earned: / 7 pointsMAT 167: Statistics, Final Exam p. 2 of 94. (2 points) Under what conditions can we approximate a binomial distribution as a normaldistribution?5. (1 point) What percent of data lies within one standard deviations of the mean as stated bythe Empirical Rule?6. (1 point) Why is it important to use random sampling?7. (1 point) A sampling distribution characterizes what type of error?8. For the following statements, determine if the calculation requires the use of a populationdistribution or a sampling distribution.(a) (1 point) Computing a confidence interval for a proportion.(b) (1 point) Computing an interval that contain 95% of individual’s weights.9. (1 point) If the normal approximation to the binomial is valid, write what the following bino-mial probability statement is approximately equal to in terms of the normal distribution.Pbinom(x > 10) ≈10. (1 point) For ANOVA, what is the distribution of the test statistic? (Give the specific name.)11. (2 points) A hypothesis test was conducted for H0: µ = 5 and Ha: µ > 5. The test statisticis t = 2.2, n = 15. Find the p-value.12. (2 points) A histogram is a useful tool that can quickly communicate many traits about a setof data. List 4 useful pieces of information that an observer can easily assess using a histogram.Instructor: Anthony Tanbakuchi Points earned: / 13 pointsMAT 167: Statistics, Final Exam p. 3 of 913. Provide short succinct written answers to the following conceptual questions.(a) (1 point) Give an example of a categorical type of variable.(b) (1 point) Which of the following measures of variation is least susceptible to outliers:standard deviation, inter-quartile range, range(c) (1 point) What percent of data is greater than Q3?(d) (1 point) What does the standard deviation represent conceptually in words? (Be concisebut don’t simply state the equation in words verbatim.)(e) (1 point) Why would a SAT percentile be preferred over a raw SAT score for collegeadmissions committees?14. (2 points) Car tires must not deform or explode when inflated up to their maximum pressurerating. Before distributing the tires, they must be tested. To test the safety of tires, aninspector randomly samples 50 tires (without replacement) from a batch of 5,000 that havebeen manufactured. The inspector inflates each of the fifty tires until they explode or deformto make sure they meet the minimum safety requirements. If none of the sampled tires failsthe test, the tires will be distributed to dealers. If the batch contains 15 defective tires thatwill explode if selected, what is the probability that the batch will be rejected?15. (2 points) If a class consists of 20 males and 8 females, what is the probability of drawing 4females without replacement?Instructor: Anthony Tanbakuchi Points earned: / 9 pointsMAT 167: Statistics, Final Exam p. 4 of 916. (2 points) You would like to conduct a study to estimate (at the 95% confidence level) theproportion of households that own one or more encyclopedias. What sample size do you needto estimate the proportion with a margin of error of 2%.17. 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) If you reject H0but H0is true, what type of error has occurred? (Type I orType II)(c) (1 point) What variable represents the actual Type I error?(d) (1 point) What does the power of a hypothesis test represent?18. Eighteen students were randomly selected to take the SAT after having either no breakfast ora complete breakfast A researcher would like to test the

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