STAT 210 Final, Fall 2003

AMER a TRAST? American University of Beirut LIRR ARY OF shiegnr STAT 910 ee eg ye nnn Introductory Statistics Fall 2003-2004 Final Exam Date: Friday, January 23, 2004 - 5:00 pm to 7:00 pm Instructor: Dr. Mohamed Kobeissi Name: ID #: Section: This is NOT an open-book exam. You are allowed to have a formula sheet and a calculator. Your exam should have 6 pages including this one. and there are 40 questions totaling 200 points. A question with more than one answer will be counted as wrong. A correct answer is 5 points. a wrong answer is -1, and an unanswered question is 0 points. Mark your answer on the answer sheet provided at the end of this exam please. Good Luck . Use the following information to answer question 1 to 3. A sample of 45 eggs yields a mean weight of 1.37 ounces. Assuming that co = 0.53 ounces . Find the margin of error in estimating yz at the 95% confidence level. A. 0.13 B. 0.02 C. 0.15 D. 6.71 E. none of the above 2. Find a confidence interval for u at the 95% confidence level. A. {1.27:1.47] — B. (0.37;2.37] ©. [1.22:1.52] Dz [1.35;1.39] —_ E. none of the above . At 95% confidence level, what sample size is needed to ensure a margin of error of 0.1? A. 86 B. 241 C. 95 D. 108 E. none of the above . The average grade for an exam is 74, and the standard deviation is 7. If 12% of the class are given A’s, and the grades are curved to follow a normal distribution, what is the lowest possible A? A. 78.6 B. 82.225 C. 92 D. 65.775 E. none of the above sn emer, JNU STWEHSI A | LiuiaRY nF RFIROT . Die A has red on one face and blue on five faces, die B has red on two faces and blue on four faces, and die C has red on three faces and blue on three faces. These are fair balanced dice. If the three dice are rolled, find the probability that exactly two of the dice come up the same color. A. 7/36 B. 13/36 C. 25/36 D. 11/36 E. none of the above . Let X have a normal distribution with o = 5. What is the mean of X if P(X < 10) =0.5. A.5 B. 10 C. 0.5 D. 5.5 E. none of the above . Use the following information to answer questions 7 and 8. Urn A contain 2 red balls and 3 blue balls, urn B contain 5 red balls and 4 blue balls. 2 balls are selected at random and without replacement from A and transferred in B. A ball is then selected at random from B. . What is the probability that the ball selected from B is red? A. 15/73 B. 29/55 C. 1/2 D. 17/110 E. none of the above . Given that the ball selected from B is red. What is the probability that the balls transferred from A to B were both red? A. 1/4 B. 3/50 C. 6/55 D. 7/58 E. none of the above . For a normal distribution with mean 41 and standard deviation 3.5, 95.44% of the population lies in what interval? A. (41,44.5) B. (87.5,41) C. (34,48) D. (37.5,48) E. none of the above . Five people are in a room. Their mean age is 30, and their median age is 25. A 40 year-old man leaves the room, and a 70 year-old woman enters. What is the mean age of the people in the room now? A. 30 B. 40 C. 70 D. 36 E. none of the above . Refer to previous question, what is the median age of the people in the room now? A. 25 B. 30 C. 36 D. 40 - E. none of the above . Use the following information to answer questions 12 to 13. Students may choose between a 3-semester-hour course in biology without labs and a 4-semester-hour course with labs. The final written examination is the same for each section. 12 students in the section with labs made an average of 84 with a standard deviation of 4 (sample 1), and 18 students in the section without labs made an average of 77 with a standard deviation of 6 (sample 2). . Using sample 2, what is the value of the test statistic that the mean y is different than 80? A. -2.12 B. 1.18 C. 0.97 D. -1.45 E. none of the above . What is the /-value. P, of the test? A.P>02 B.0.02<P<005 C.P=002 D.P<90.005 E. none of the above ve ema a wy 'CRRSIYL LIBRARY oF actADT Consider now the two samples as independent samples from different normal populations to answer questions 14 to 22. . What are the null and alternative hypotheses to test that the lab has improved exam scores? i) Ho: wy = pe vs. Ha: jy < po ii) Ho: pa = pe vs. Ho: pr > pe ili) Ho: 1 = we vs. He: wy # pe iv) Ho: wi — wo = 84 vs. He: wy — po # 84 A. (i) B. (ii) C. (iii) D. (iv) E. none of the above . Assuming equal population variances, what is the pooled standard deviation? A. 3.28 B. 4.85 C. 5.3 D. 0.96 E. none of the above . Assuming equal population variances, what is the value of the test. statistic for Ho : uy = LU? A.1.9 B. -2,12 C. 47 D. 3.54 E. none of the above . Assuming equal population variances, what is the P-value, P, of the test? A. P >0.2 B.0.05<P<01 C.P=0.02 D. P< 0.005 E. none of the above . For testing that the curriculum has improved the exam scores. at what significance level would the null hypothesis be rejected? i) At the 0.5% significance level ii) At the 0.2% significance level iii) At the 0.1% significance level iv) At any significance level A. (i) B. (ii) C. (it) D. (iv) E. none of the above . Assuming equal population variances, find a 99% confidence interval for the difference be- tween the two means ,4) — 22. A. [2.12:3.26] B. [1.54:12.45} — C. [-1.3;2.6] D- [0:1.72] E. none of the above . Assuming unequal population variances, what is the degree of freedom for Ho : py = pug? A. 14 B, 28 C. 15 D. 27 E. none of the above . Assuming unequal population variances, what is the value of the test statistic for Hy : 4, = pin? A. -1.56 B. 4.78 C. 2.63 D. 3.85 E. none of the above . Assuming unequal population variances, what are the critical values for testing Hq: 1 = ple vs Hy : 1 ¥ pe, with a = 0.1? A. +1.753 B, 1.697 C, £1.314 D. 41.310 E. none of the above faves i i Litoary IV. Use the following information to answer questions 23 to 25. Scores on an aptitude test are normally distributed with a mean of 220 and a standard deviation of 30. 23. For a random sample of size 50, what is the mean of the variable =? A. 30 B. 170 C. 50 D. 220 E. none of the above 24. For a random sample of size 50. what is the standard deviation of the variable #? A. 50 B. 30 C. 4.24 D. 212.13 E. none of the above 25. What is the probability that the sampling error made in estimating the population mean by the mean of a random sample of 50 test scores will be at most 5 points? A. 0.135 B, 0.762 C. 0.999 D. 0.881 E. none of the above 26. For the population of one town, the number of siblings is a random variable whose relative frequency histogram is left-skewed. Let Z denote the mean number of siblings for a random sample of size 45. For samples of size 45, which of the following statements concerning the sampling distribution of the mean is true? i) F is normally distributed. ii) The distribution of Z is left-skewed. iii) Z is approximately normally distributed. iv) The distribution of 7 is approximately left-skewed. A. (3) B. {ii) C. (iii) D. (iv) E. none of the above 27. Suppose you have obtained a 95% confidence interval for . Which of the following statements is/are true regarding the relationship between precision and confidence level? Assume the sample size is fixed. i) Increasing the confidence level to 99% will result in a narrower interval. “#ii) Decreasing the confidence level to 90% will result in a greater precision. iii) Decreasing the precision will result in a higher confidence level. iv) Increasing the precision will result in a higher confidence level. A. (ii) and (iii) B. (i) and (iv) C. (it) and (iv) D. (i) and (iii) E. none 28. Suppose that scores for men on an aptitude test has greater standard deviation than scores for women on the same test. Based on a sample of size 50, a 95% confidence interval form the mean score, j4, of all women has a margin of error of 2.2. Which of the following confidence intervals will have a smaller margin of error? i) A 99% confidence interval for the mean score of women. Sample size 50. ii) A 95% confidence interval for the mean score of women. Sample size 100. ili) A 95% confidence interval for the mean score of men. Sample size 50. A, (iii) B. (ii) C. (i) D. (i) and (ii) and (iii) E. none of the above eapentie Oe eee MERICAN CNIVENSIT LIBRARY | OF BFIROT \ — . Use the following information to answer questions 29 to 31. 3 persons are to be selected from a group of 10 married couples. . In how many way can this be done if there is no restrictions? A. 180 B. 120 C. t140 D. 960 E. none of the above - In how many way can this be done if a married couple cannot be selected? A. 120 B. 960 _C. 1140 D. 180 E. none of the above . In how many way can this be done if the group must contain a married couple? A. 1140 B. 120 C. 960 D. 180 E. none of the above . Sam and Jad play a game in which Sam’s chance of winning is 2/3. In a series of eight such games, supposedly independent, what is the chance that Sam will win at least six? A. 0.35 B. 0.47 C. 0.71 D. 0.56 E. none of the above . Refer to previous question, what is the expectation of winning for Sam? A. 16/9 B. 8/3 C. 16/3 D. 8/9 E. none of the above . If the testing of Ho: 1 — po vs Ha : py) # pe at significance level a results in not rejecting Ho, then which of the following is true? i) A one tailed test will reject Hg at significance level a. ii) The hypothesized value will lie in a (1 — a)100% confidence interval for y? iii) The hypothesized value will not lic in a (1 — a)100% confidence interval for p? iii) The observed value will not lie in a (1 ~ a@)100% confidence interval for ju? A. i) B. ii) C. ii) D. iv) E. none of the above . A variable of two populations has mean 49 and standard deviation 12 for the first and mean 18 and standard deviation 8 for the second population. For independent samples of size 5 from population 1 and 14 from population 2, determine the standard deviation of ; — Zo. A. 5.78 B. 4.92 C. 1.72 D. 33.37 E. none of the above . Suppose that [34.2; 38.4] is a 99% z-distribution confidence interval for a population mean based on sample of size 50. What is the sample mean? A. 38.4 B. 36.3 C. 72.6 D. 34.2 E. none of the above . Refer to previous question, what is the population standard deviation? A. 7.57 B. 9.05 Cc. 8.9 D. 5.76 E. none of the above . For a right tailed one-sample z-test. the value obtained for the test statistic was 0.75. Deter- mine the P-value, P. A. 0.7734 B. 0.5468 C. 0.2266 D. 0.4532 E. none of the above 39. 40. pw JAweDu ce an Yop ti rary In the past. the mean running time for a certain type of flashlight battery has been 9.2 hours. The manufacturer has introduced a change in the production method and want to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypothesis are Ho : 4 = 9.2 hours and H, : # > 9.2 hours. Explain the meaning of a type II error. i) Concluding that yz: > 9.2 hours when in fact ft > 9.2 hours. ii) Failing to reject the hypothesis that fs = 9.2 hours when in fact 4 > 9.2 hours. ili) Concluding that p > 9.2 hours when in fact ii = 9.2 hours. lil) Failing to reject the hypothesis that 2 = 9.2 hours when in fact p= 9.2 hours. A. i} B. ii) C. iii) D. iv) E. none of the above The average weight of sardines caught at cheat lake is 35 grams with a standard deviation of 4 grams. What is the probability that the mean of a sample of 64 sardines will exceed 36 grams? A. 0.456 B. 0.9544 C. 0.0228 D. 0.0026 E. none of the above Answer sheet ane ere a et ED oN es 8 re RYE HBR ARY oS @ia0T Question Answer Question | answer 1. 2. 21. 22.