SOLUTIONSMAT 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 15 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 SOLUTIONS p. 1 of 15Solution: Exam Results:> summary ( s c o r e )Min . 1 s t Qu. Median Mean 3 rd Qu. Max.22 . 54 78 . 87 84 . 51 78 . 11 92 . 25 10 0. 00> par ( mfrow = c ( 1 , 2 ) )> box plo t ( sc o re , main = ”Boxplot o f exam s c o r e s ”)> h i s t ( s co re , main = ”Histogram o f exam s c o r e s ”)●●●20 40 60 80 100Boxplot of exam scoresHistogram of exam scoresscoreFrequency20 40 60 80 1000 2 4 6 8Comparison of midterm average to final exam grades (for those who took the final):> p l o t ( midterm , f i n a l , main = ” Fi n a l Exam vs Midterm Ave Exam Grades ”)> co r . t e s t ( midterm , f i n a l )Pearson ' s product−moment c o r r e l a t i o ndata : midterm and f i n a lt = 3 . 1 1 5 2 , df = 11 , p−v al ue = 0.0 09 834a l t e r n a t i v e h y p o t h e s i s : t ru e c o r r e l a t i o n i s not equa l to 095 p er c e n t c o n f i d e n c e i n t e r v a l :0.2 145 887 0 .89 717 90sample e s t i m a t e s :co r0.6 84 627> r e s = lm ( f i n a l ˜ midterm )> r e sC a l l :lm ( formula = f i n a l ˜ midterm )C o e f f i c i e n t s :( I n t e r c e p t ) midterm18 .19 68 0. 79 48> a b l i n e ( r e s )Instructor: Anthony Tanbakuchi Points earned: / 0 pointsMAT 167: Statistics, Final Exam SOLUTIONS p. 2 of 15●●●●●●●●●●●●●30 40 50 60 70 80 90 10020 40 60 80 100Final Exam vs Midterm Ave Exam GradesmidtermfinalOverall Course Grades (for those who took the final):> summary ( s c o r e )Min . 1 s t Qu. Median Mean 3 rd Qu. Max.36 . 70 80 . 20 82 . 50 80 . 78 93 . 90 98 . 50> par ( mfrow = c ( 1 , 2 ) )> box plo t ( sc o re , main = ”Boxplot o f o v e r a l l c o u r s e gra de s ”)> h i s t ( s co re , main = ”Histogram o f o v e r a l l c ou r s e g r a de s ”)●●40 60 80 100Boxplot of overall course gradesHistogram of overall course gradesscoreFrequency30 50 70 900 1 2 3 4 5 61. 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 plotInstructor: Anthony Tanbakuchi Points earned: / 0 pointsMAT 167: Statistics, Final Exam SOLUTIONS p. 3 of 159. 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.Solution: Conduct a study and construct a confidence interval for a mean.(b) (1 point) A researcher wants to determine if bear weights are normally distributed.Solution: Plot the data with a histogram and see if it looks like a normal distribution.If there are no outliers and it does not appear skewed, then closely analyze it with aQ-Q norm plot. The data should fall close to a line on the Q-Q norm plot if it has anormal distribution.(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, . . . ).Solution: Use the test of homogeneity. The researcher needs to determine if theproportion of students graduating in the different economic classes are the same or ifat least one is different.(d) (1 point) A farmer wants to determine if the mean crop yield is the same for eight differentbrands of fertilizer.Solution: Use 1-way ANOVA. H0: mean crop yield is equal for all eight brands. Ha:mean crop yield is different for at least one brand.(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.Solution: Use a two sample hypothesis test of proportions. H0: p1= p2, Ha: p1<p2. (Let group 2 be the control.)2. (1 point) What test is a many sample generalization of the two sample t-test?Instructor: Anthony Tanbakuchi Points earned: / 6 pointsMAT 167: Statistics, Final Exam SOLUTIONS p. 4 of 15Solution: 1-Way ANOVA3. (1 point) If the mean, median, and mode for a data set are different, what can you concludeabout the data’s distribution?Solution: The distribution is not symmetrical, it is skewed.4. (2 points) Under what conditions can we approximate a binomial distribution as a normaldistribution?Solution: If the requirements for a binomial distribution are met, it can be approximatedas a normal distribution when : np, nq ≥ 5. In words, there must be at least five successesand failures.5. (1 point) What percent of data lies within one standard deviations of the mean as stated bythe Empirical Rule?Solution: 68%6. (1 point) Why is it important to use random sampling?Solution: …