1 BUEC 333 Spring 1987 D. Maki MIDTERM EXAMINATION This examination consists of 20 multiple choice questions, with a value of 5 points each, for a total of 100 points on the examination. Choose the letter corresponding to the one best answer to each question. Your grade will be computed on the basis of the number of correct answers. The exams will be machine graded, and making the answers legible to the machine is your responsibility. Use soft pencil (HB or softer) only. Fill in your name in the appropriate circles on the back of the answer sheet. This is a closed book examination - no notes are allowed. A formula sheet and tables are attached. Total time allowed = 50 minutes. Questions 1 and 2 relate to the following problem setting: Hi-note Company makes a line of notebooks for the college market. Notebook line C consists of 100 pages and the manufacturer regularly draws samples of 25 books to test if they deviate from the 100 pages. One sample showed a mean, xbar, of 95 pages and standard deviation, S, of 10 pages. 1. The appropriate value for the test statistic is: a. 2.0 b. -2.0 c. 2.5 d. -2.5 e. 10.5 2. The rejection (critical) value for the proper test if alpha = .05 is: a. 1.318 b. 1.711 c. 1.960 d. 2.064 e. 2.576 Questions 3 and 4 relate to the following problem setting. (NOTE: THIS REFERS TO CHAPTER 15 - NOT COVERED in 1997) A prospective investor samples 12 financial institutions, grouped in four categories, to determine if yields vary by type of institution. The data are given below. Group Banks Trusts Credit Unions Mutuals 4 4 6 8 3 5 6 9 5 3 12 7 Sum 12 12 24 24 Mean 4 4 8 8 3. The between groups mean square value from the financial institution sample data is: a. 48.00 b. 10.00 c. 12.00 d. 5.33 e. 16.00 4. The within groups mean square value from the financial institution sample data is: a. 48.00 b. 30.00 c. 3.75 d. 10.00 e. 16.00 Questions 5 and 6 relate to the following problem setting. The data in the following table are to be used to test whether the population from which they were drawn is Normal, at the alpha = .05 level. Class Limits Observed Frequency Less than 10 9 10 < 25 22 25 < 50 35 50 < 75 39 75 < 90 21 90 or more 8 Assume it was calculated from the raw data in the sample that xbar = 50 and S = 20. 5. The expected frequency under the null hypothesis for the class "10 < 25" is: a. 3.1 b. 8.3 c. 11.1 d. 14.2 e. 23.6 6. The appropriate rejection (critical) value is: a. 7.81 b. 9.35 c. 9.49 d. 11.14 e. None of the above. 7. Given the following data: (X: 2, -1, 0.5; Y: 2.5, 4), compute the V statistic for the rank sum test. a. 1.5 b. 2.5 c. 3.5 d. 4.5 e. 5.0 Questions 8, 9 and 10 relate to the following problem setting. Five skilled workers each assemble one unit of output using an "Acme" riveting gun, and another unit of output using an "Apex" riveting gun. The time (in minutes) it took them to complete the task is given below. Worker Acme Apex Smith 25 30 Jones 30 25 Fisher 15 20 Grant 12 17 Olson 35 40 The hypotheses to be tested are: Ho: mean-Acme greater than or equal to mean-Apex, HA: mean-Acme < mean-Apex. 8. Using the sign test, the appropriate p-value is (use the Binomial table or Binomial formula - not the Normal approximation): a. 0.0313 b. 0.2188 c. 0.1562 d. 0.1875 e. over 0.50 9. Using the appropriate parametric test, the calculated value of the test statistic is: a. 0.67 b. 1.50 c. 2.36 d. 2.52 e. 3.00 10. Using the Wilcoxon test, the calculated value of the test statistic is: a. 0.16 b. 0.67 c. 1.21 d. 1.65 e. 3.00 11. Paired comparisons can give greater precision of estimation than group comparisons, but only if pairing is effective. To be effective the pairs must be such that the: a. variation among the pairs is greater than the variation between the units within the pairs. b. variation among the pairs is less than the variation between units within the pairs. c. variation among the pairs is equal to the variation between the units within the pairs. d. mean of group one be greater than the mean of group two. e. mean of group one be less than the mean of group two. 12. When only two groups are being compared using the Chi- square test, it is equivalent to: a. a Binomial situation b. testing for a difference between two population proportions c. a Z test d. all of the above e. none of the above Questions 13 and 14 relate to the following problem setting. A random sample of 200 voters was selected from all registered voters in a certain city, and 175 of these voters indicated that they planned to vote for Mr. Green for Mayor. Mr. Green, however, has made a public statement that he expects to get at least 90% of the vote. 13. The appropriate test statistic is: a. -2.000 b. -1.1785 c. -1.0690 d. -0.025 e. 2.000 14. The critical value for the proper test if alpha = 0.05 is: a. 1.645 b. -1.645 c. 1.96 d. -1.96 e. 0.05 15. The probability of Type I error, alpha, and the probability of Type II error, beta, have the relationship: a. alpha + beta = 1 b. if alpha increases, beta also increases c. alpha/beta = a constant d. if alpha is nonzero, beta is also nonzero e. if alpha is nonzero, then beta = 0 Questions 16 and 17 relate to the following problem setting. Independent random samples of size 10 are selected from each of two populations. The sample means are calculated to be 10 and 12.5, respectively. The sample standard deviations are also calculated, and these values are 2 and 4, respectively. 16. Testing whether the two means are equal, the absolute value of the test statistic is: a. 0.25 b. 4.00 c. 2.00 d. 2.50 e. 1.77 17. Testing to determine if these two populations have equal variances at the alpha = 0.05 level, the appropriate critical value is: a. 3.1789 b. 1.96 c. 1.645 d. -3.1789 e. 4.026 18. In screening for possible cancer cases, Ho: is "this patient does not have cancer". Which of the following is the most dangerous? a. Ho: is false and it is accepted b. Ho: is false and it is rejected c. Ho: is true and it is accepted d. Ho: is true and it is rejected e. type I error Questions 19 and 20 relate to the following problem setting: Testing Ho: sigma-squared less than or equal to 53.2; HA: sigma-squared > 53.2 with n = 20 at the alpha = 0.01 level, we find S-squared = 76.16. 19. The correct conclusion is: a. accept Ho: because 27.20 < 36.19 b. reject Ho: because 27.20 < 36.19 c. accept Ho: because 27.20 < 30.14 d. reject Ho: because 27.20 < 30.14 e. accept Ho: because 30.14 < 36.19 20. If sigma-squared = 70.783, what is beta? a. zero b. approximately 0.50 c. 0.90 d. over 0.90 e. impossible to determine from the information given. END OF EXAMINATION