Final Exam - Spring 2005 | Introduction to Statistics | STAT 1222, Exams of Statistics

Download Final Exam - Spring 2005 | Introduction to Statistics | STAT 1222 and more Exams Statistics in PDF only on Docsity! STAT 1222 Spring 2005 Common Final Exam May 5, 2005 PLEASE PRINT THE FOLLOWING INFORMATION: Name: Instructor: Student ID: Section/Time: THIS EXAM HAS TWO PARTS. . PARTI. Consists of 25 multiple choice questions worth a total of 60 points: Read all questions carefully. You may do calculations on the test paper. Mark the number of the opscan sheet corresponding to the test question number with a Number 2 pencil or a mechanical pencil with HB lead. Mark only one answer; otherwise the answer will be counted as incorrect. In case there is more than one answer; mark the best answer. Please make sure that your name and ID appear on the opscan sheet in the spaces provided. PART IL so : This part consists of 3 problems (40 points in total). You MUST show all the work for each question in the space provided to receive full credit for that question. If you write your explanations in another part of the test, please indicate accordingly. At the end of the examination, you MUST hand in this test booklet, your answer sheet and all scratch paper. : FOR DEPARTMENTAL USE ONLY: _ PARTIE , Questions 1 . 2 3 Score Part I Part I TOTAL  STAT 1222 FINAL EXAM __ SPRING 2005 ” Use the following information to answer questions 5 and 6. The table below shows the results of a survey in which researchers examined a child’s IQ and the presence of a gene in the child. ‘| Gene present | Gene not ‘present | Total High IQ 33 19 52 Normal IQ 39 11 50 Total 72 30 102 5. The probability that a randomly selected child has High IQ is closest to a) 47 71 234 67 (e) .51 Sage §. The probability that a randomly selected child has Normal tg and Gene Present is closest to (a) 49 (b):.71 (c) .29 (a) .38 (e}) .46 Use the following information ta answer questions 7 and 8. Let X = number of children under 18 years of age in an American family: According to -the Mumbo Jumbo Society of the Unites States, in 1993; the probability distribution of X was found to be: z 0 f a Ts Tt Te P@) (812) 20 ae 7. The proportion of American families that have 2 or more children under 18 is a) Lb) 81. c) 89d) .20— se) at  STAT 1299 FINAL EXAM SPRING 2005 8. The expected number of children under 18 years of age in an American family is a) 1b) 99 c) 15 4d) 3° e) 48 : Use the following information to answer questions 9 and 10, and 11. The U.S. Environmental Protection Agency publishes figures on solid waste generated in the United States. Suppose that during a year, the daily amount of solid. waste generated per person was normally distributed with a mean of 3.58 ‘Pounds and a standard deviation of 1.04 pounds. 9. The probability that a randomly selected a person in the U.S. generates between 2 and 4 pounds is closest to (a) .3095 (b), .4649 (c) .1554 (a) .0351 * (e) 5911 10: If 50 U. s. residents are randomly selected, approximately how many. are expected to. generate less than 3 pounds.of solid waste per day? (a). 23 “(b) 8 (c) 15. (a) 10 (2) 30: ° il. To be in the top 10% of solid waste producers, a person must be producing at least (a) 3.5 pounds per day (b) 4.9 pounds per day (c) 5.8 pounds per day - (d) 3.8 pounds per day (e) 10 pounds per day  STAT 1222 : FINAL EXAM. SPRING 2005 15. All other information remaining unchanged, which of the following would produce a wider interval than the 90% confidence interval constructed above? (a) A sample of size 28 instead of 20. (b) A sample of size 24 instead of 20. (c) An 80% confidence interval rather than a 90% confidence interval (d) A sample with a standard deviation of 525 instead of 677. (e) A sample with a standard deviation of 725 instead of 677. 16. Suppose that we are interested in estimating the mean age, p, of ‘all people in ‘the civilian labor force in. the United States. How large a sample should we use to estimate u to within 0.5 year at a 95% confidence level? Use o = 12, 17. A random sample of 1010 U.S. employees was chosen and' asked whether they "play hooky", that is, call in sick at. least once a year when they simply need time.to rélax; 202 responded "yes". Use this information to set up a 95% confidence interval for the proportion, p, of all U. 8, employees who play hooky... (a) (0.184, 0.216) (by (0.171, 0.202) (c) (0.188, 0.232) (a) (0.175, 0.225) () (0.170, 0.221) Use the following information to answer questions 18 - 19. A researcher wants to test the hypothesis Hp : < 100 vs Ha 2 > 100. She takes a sample of size n = 80 and finds s = 10 and # = 102.5. - 18. The standardized test statistics for this test is closest to .  STAT 1222 FINAL EXAM — SPRING 2005 22. Find the value of the standard test statistic for this problem. (a) z= 1.322 (b) z= -1.322 (c) z = 0.06 (d) z= ~0.06 (e) 2=—29.14 23, Find the rejection region at a = 0.1 (a) z<=1.96 or z > 1.96 (b) 2> 1.96 (c) 2<—1.645 or-z > 1.645 (d) z> 1.645 {e) z< —1.28 Use the following information to answer questions 24 - 25. ) ) A manufacturer claims that the average calling range (in feet) for its 2.4-GHz cordless telephone is greater than that of its leading competitor. You perform a study using 14 randomly selected phones from the manufacturer and 16 randomly selected similar phones from its competitor. The results are shown in the table below. Assume the populations are normally distributed and the population variances are equal. Manufacturer Competitor B,=1275 By = 1250 8 = 45 8q = 30° 24, Set up the null and alternative hypotheses to test the manufacturer's claim. a) Ho f fy -= fy versus Hy: py Ff py b) Ho: py 2 py versus Hy : jy < py (c) Ho: fy S Mp versus Ha : py > by (d) Ho? Z1"< Se versus Hy : Z, > Fy (8) Ho: fly > ply versus Hy: uy F ply 25. Find the value of the standardized test statistics. (a) t= -1.581 (b) ¢ = 2.370 () #= 1.763 (a) = 1.811 (e) t= -1.763  STAT 1222 FINAL EXAM _- SPRING 2005 PART II FREE RESPONSE QUESTIONS 1. Harper’s Index claims that 32% of Americans are in favor of outlawing cigarettes. You decide to test this claim and ask a random sample of 200 Americans whether they are in favor of outlawing cigarettes. Of the 200 Americans, you find 54 in favor. At @ = 0.05, is there sufficient evidence to conclude that less than’ 32% of American are in favor of outlawing cigarettes? (a) Conduct a test of hypothesis by showing your work in the following four steps. StepI Hy: Step II. Standardized statistic and its value Step IIi. Decision rule Step IV. Conclusion ” Spring 2005 The use of a TI-89 or T1-92 calculator 0 on this test is a violation of : the Code of, Student Conduct:  3. As people age they begin experience hearing loss. A study was done on a random sample of 8 subjects to determine "comfort level" of sound and age in people. The data are given here: Age z Sound level y (years) (decibels) 15 56 25 57 35 64 45 64 55 - 68 65 : 74. i>) 78 85 85 De=400 y= 546 Say = 29,010 . Sox? = 24,200 © Sry? = 37,986 (a) Assuming the existence of a linear relationship between comfortable sound level and age, find the equation of the regression line relating y to x. (b) Find the standard error of estimate. (c) Predict the comfortable level of sound for a.60 year old person. (d) Construct a 90% prediction interval for the comfortable level. of sound for & 60 year old person. . . 10>  INFERENCE ABOUT TWO POPULATION MEANS: TEST STATISTIC CONDITIONS Independent samples, n, > 30,n2 > 30 = Aa tee) , mm Teg Independent samples, normal populations Ny OF M2 < 30; of, oF not equal te G — abe “an 2) . 1 2 Ving me with d.f. = smaller of (my — 1) and (ng 1) Independent samples, normal populations ta (@1. = B2) = (2 — He) Ny OF M2 < 30; of, oF equal - — . . (rig — 15? + (mg —1)82 fT TT A fg ny tng —-2 hy owith d.f.=ny+ing— . cations d— pg Dependent samples; normal populations = oa 8a//n CORRELATION AND REGRESSION: Corrélation Coefficient: 7 = ~ nQozy ~ Ol #)(009) : ny x? — t-test for Correlation Coefficient: + = Equation of a Regression Line: 9= mz +b _ RL ey — (Oo 2)( ( y) nia? —(d 2)? Standard Error of estimate: . s, =f m SSBF _ co Prediction Interval for y when x = 2 : xv —B)? 144 SEO Say O~ beSe <y y <o+he, Quah /n le oy? rT 5 with df=n=2- —Tf n-2 b=§G ma LY ~ bv y= my ay nm) no — < itt nt nea? ay  Standard Normal Distribution (continued) 3.4.| 9007 19997 .9997  : sue ” &Distribution i ¢-confidence interval t + t f t -t - t Left-tailed test Right-tailed test Level of . confidence, ¢ 0.50 0.80 0.90 0.95" 0.98 0.99 One tail, w. 0.25 010 - 0.05 0,025 00% 0.005 df... Two tails,a -| 0.50 "0.20 O10. O05. 0.02 Q.01 12.706 31.821 63.657 3.365 4.032 2,821 3.250 Two-tailed test