STAT 400 Exam 3 - Problem Solutions - Prof. Mcblaine Michael Boyle, Exams of Probability and Statistics

Download STAT 400 Exam 3 - Problem Solutions - Prof. Mcblaine Michael Boyle and more Exams Probability and Statistics in PDF only on Docsity! STAT 400—EXAM 3 August 22,1997 Work each numbered problem on a separate answer sheet. (You may use both front and back of each sheet.) Show all work on problems 2-4: partial credit may be given for wrong answers if the method shown is essentially correct. Correct answers without adequate supporting work may receive no credit. 1. For each of the following problems (a-e) choose from the list on the right (a) the type of problem (choices A-E), (b) the random variable or statistic used (choices F-R) and (c) the distribution involved together with the degrees of freedom where appropriate (choices S-V). Do not compute numerical answers. Your answers should consist of three letters and the degrees of freedom for all but the normal distribution. (9) a. A random sample of 100 students from a college showed an average IQ score of 112 with a standard deviation of 10. Establish a 95% confidence interval estimate of the mean IQ score of all students attending the college. (9) b. A circuit fuse is designed to burn out as the electric current reaches 20 amperes. From a lot of 10,000 fuses 36 are selected and tested for their breaking point. What do you conclude about the amperage specification of the lot if the sample reveals a mean of 20.9 amperes and a standard deviation of 1.5 amperes? (9) c. An examination is going to be used to place all new students in the mathematics courses of a university. The department gives the test to 150 incoming freshmen and transfer students and finds that the mean is 60. They also want to estimate the standard deviation for the test so that they can set the cut-off points for the various classes. (9) d. The nicotine contents of five cigarettes of a certain brand measured in milligrams are 21, 19, 23, 19, 23. Establish a 99% confidence interval estimate of the average nicotine content of this brand of cigarette. (9) e. Two hundred and fifty-six patients suffering from a certain disease were treated with a newly developed drug. The drug was effective in curing 128 of these cases, With what degree of confidence can we assert that the efrectiveness of this drug is between 45% and 55%. 2. A superintendent of schools has read in a journal that, on the average, elementary-school children watch 15 hours of television per week. She feels that children in her school district watch less. To test this hypothesis, she randomly selects from the school files the names of 49 elementary-school children and asks the parents about their children's television-watching habits. The sample mean of television time is 10 hours and the sample standard deviation is s = 5 hours. (is) a. What can she conclude from the dam using a .01 level test? In answering this question, state clearly the null and alternative hypotheses for this situation, the test statistic used, the distribution of the test statistic, and the rejection region. (6) b. What is a type II error in this situation? What is the probability of a type II error occuring with \i = 11 ? (6) c. What assumptions would have to be made if the superintendent used a sample of 20 children? What changes would have to be made? You do not have to carry out all the computations but you do need to state clearly where changes have to be made and what the changes are. A. Point estimation B. Interval estimation C. Sample size estimation D. Hypothesis testing one-tailed test E. Hypothesis testing two-tailed test _. '~~~~ ~ F. X = G. p = X/n H. Xj - X2 J. X- K, a/Vn X-MO S/Vn L. P-PO VPoO-P())/n (n-l)S2 a2M. N. X±za/2 () Vn O. X±za/2 (-|z) Vn P. X±taJ2 (~) Vn Q. S. Normal T. t with __ degrees of freedom U. Chi-square with __ degrees of freedom V. F with __ and __ degrees of freedom PLEASE TURN OVER FOR PROBLEMS 3 AND 4.