Download Stats Midterm II - Binomial Dist., Confidence Intervals, Hypothesis Testing & Probability and more Exams Statistics in PDF only on Docsity! Page 1 of 5 Statistics - OR 155, Section 2, Midterm II Tuesday, April 10, 2007 Name: _______________________________________________________ Pledge: I have neither given nor received aid on this examination. Signature: _____________________________________________________ Instructions: Do not do any actual numerical calculations (e.g. answers in a form that you would type into an Excel field, with a working answer, are expected). 1. [16] In each situation below, is it reasonable to use the binomial distribution, for the random variable X? Give brief reasons in each case. If a binomial distribution applies, the parameter values. a. Phone calls made at random in a survey, reach a live person only 1 time in 15. A surveyor continues calling until he succeeds in reaching a live person. X is the number of calls made until success. b. Geese arrive to foul the pond of an apartment complex at the rate of 10 per hour. X is the number of geese that arrive over the next two hours. c. 20% of attempted logins to a system fail, and these attempts are independent. Because of Darci’s busy schedule, there are only 5 times over the weekend, when she will have a chance (and only one chance each time) to try to log in. X is the number of times that she successfully logs in. d. A pool of 100 potential jurors is chosen at random from a small city with only 500 adult residents. 60% of residents in this city support the death penalty. X = the number of death penalty supporters in the pool. Page 2 of 5 2. [20] A bank of 10 Radon detectors were tested in a chamber where the known concentration of radon was 85 (PCi/L). The average concentration measured by the 10 detectors was 89 (PCi/L). Page 5 of 5 4. [20] To study the effects of piano lessons on spatial-temporal reasoning, 5 pairs of identical twins were split, with one twin receiving the piano lessons, and the other not. Results on a reasoning test after 6 months, were: A B C D E F 1 Piano Lessons 35 78 53 66 40 2 No lessons 24 73 51 61 39 a. Formulate hypotheses (in terms of stated population parameters), to investigate the hypothesis that piano lessons have a positive effect on spatial temporal reasoning. b. Write an Excel command to give a P-value for the hypothesis test in (a). c. If the answer to (b) is 0.004, give a yes-no interpretation. d. If the answer to (b) is 0.004, give a gray-level interpretation. e. If it was later discovered that due to a clerical error, twins were not actually used in the study, and in fact there was no relation between the children within the above pairs, then give an appropriately modified version of your answer to (b). Page 6 of 5 5. [20] On a multiple choice test each student has probability p of getting a question right, and questions are independent of each other. Abby is a good student, for whom p = 0.8. A test is given with 100 questions. Let X = Abby’s score = # of correct answers. a. What are the mean and standard deviation of the distribution of Abby’s scores? b. What is the exact P{X ≥ 70}? c. Why is the Normal approximation appropriate to answer (b)? d. Give a naïve Normal approximation answer to (b). e. Give an answer to (b), which uses the Normal approximation with continuity correction.
