1BUEC 333 Summer 2002 D. Maki MIDTERM EXAMINATION - A Important - record on the top front of your answer sheet the letter "A", "B" or "C" from the examination title above. This examination consists of 15 multiple choice questions, with a value of 5 points each, for a total of 75 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 the appropriate circles corresponding to your name on 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. Infinite populations are assumed in all questions where population size is relevant. 1. (Warning: this is a tricky question - read carefully). You want to test the hypothesis that interest rates and inflation rates are independent (Ho:). The following is partial sample data available in the form of a 3 by 3 contingency table: Inflation Rates Interest Rates 2-6 7-10 11-20 Total 2-6 10 7-10 36 11-20 50 Total 5 40 100 On the basis of this information (and assuming that cells will not have to be joined together), we can conclude that: a. Ho: cannot be rejected at alpha=10% b. Ho: cannot be accepted at alpha=10% c. before testing Ho:, we need to obtain a 2 by 2 contingency table d. there is clearly not enough information to determine if Ho: needs to be accepted or rejected e. none of the above 2. Suppose that we have a normal distribution and we test the null hypothesis Ho: that the population mean = 10 against a two-tailed alternative. The significance level of the test is alpha. It is given that z(alpha)=4 and z(alpha/2)=6, sigma=10 and n=100. If the sample mean is found to be 3, then a. we do not reject Ho: b. we reject Ho: c. we cannot reach a decision based on the information given d. we rejct Ho: only if the z statistic is greater than 100 e. none of the above. 3. Testing the null hypothesis that two means are equal against a two-tailed alternative, we have two different situations: (1) both variances are known and the variance of the difference between the two sample means is 20, (2) both variances are estimated from the samples, and the estimated variance of the difference between the two sample means is 20. Then, for a given alpha, a. whenever we accept Ho: in case (1), we accept Ho: in case (2) b. whenever we accept Ho: in case (2), we accept Ho: in case (1) c. there is no definite relationship between the accept-reject decision in the two cases d. we get the same decision in the two cases e. none of the above 4. The interest paid in Bank A and in Bank B in a sample of various months is given by: Bank A Bank B 5 4 5.5 8 6 The Mann-Whitney U statistic is: a. 0 b. 1 c. 2 d. 3 e. different depending on which sample you work with 5. The prices of six products at two supermarkets were: Product Store A Store B 1 $1.00 $1.25 2 2.10 2.15 3 2.75 2.75 4 3.00 3.10 5 3.25 3.35 6 3.75 3.76 Using a two-tailed sign test at the alpha = 5% level, we conclude: a. store B is significantly more expensive b. though store B is more expensive, the difference is not significant c. we cannot use the sign test where there is a tie d. the assumptions for using the sign test are not met here e. none of the above 6. In EXCEL, the simplest way to test whether two populations have equal variances is to use the Two-Sample F-Test for Variances, under Data Analysis from the Tools menu. The next simplest way would be to use: a. the t-test: Two-Sample Assuming Unequal Variances function b. the t-test: Two-Sample Assuming Equal Variance function c. the information from the Descriptive Statistics function d. Two-Factor ANOVA Without Replication e. Two-Factor ANOVA With Replication 7. We are conducting a test of a single mean, variance known, with the null hypothesis that Mu <= 100 using an alpha level of 5%. We decide to reject the hypothesis if xbar is greater than 110. If the true mean is 112, what is beta (the probability of type II error)? a. over 50% b. between 40 and 50% c. between 30 and 40% d. between 20 and 30% e. less than 20% 8. Testing the hypothesis that two means are equal when the variances are unknown, the following data are available: First sample Second sample 3 4 4 5 4 5 5 6 The value of the calculated test statistic is: a. 6.0 b. 3.4 c. 3.0 d. 1.7 e. 1.5 9. A Wilcoxon signed rank test is being employed to see whether a certain drug lowers blood pressure. Before and after readings were taken for n=20 subjects, and differences calculated by subtracting "after" readings from "before" readings. There were four ties. T=39 turned out to be calculated from positive differences. Hence the conclusion is: a. reject Ho: at alpha=0.10 but not at alpha=0.05 b. reject Ho: at alpha=0.05 but not at alpha=0.01 c. reject Ho: at alpha=0.01 but not at alpha=0.005 d. reject Ho: at any alpha less than 0.10 e. none of the above 10. You want to test the hypothesis that patients arriving at a certain clinic have a Poisson arrival distribution. A test shows the following results: Arrivals in a 15-minute period Frequency 0 20 1 40 2 40 The expected frequency for the first category (i.e. zero arrivals) is: a. 40.00 b. 13.13 c. 20.00 d. 12.30 e. 30.12 Questions 11 and 12 refer to the following problem setting. The production (units assembled) of the three employees before lunch and after lunch has been recorded as follows: Employee Before Lunch After Lunch Velma 10 8 Fred 8 7 Daphne 6 6 11. Testing the one-tailed hypothesis that the difference in means in lower after lunch, the calculated test statistic is: a. zero b. 1.00 c. greater than 1.00 and less than or equal to 2.00 d. greater than 2.00 e. none of the above 12. Testing the two-tailed hypothesis that the variances of Before Lunch and After Lunch are equal, the calculated test statistic is: a. zero b. 1.00 c. greater than 1.00 and less than or equal to 2.00 d. greater than 2.00 e. none of the above 13. Beta, the probablility of type II error: a. only makes sense in tests using the z distribution b. applies to all tests except those using the binomial distribution c. is irrelevant in "real world" use of statistics d. is unpredictable before the fact and undecipherable after the fact e. none of the above 14. Which of the following is a true statement? a. A null hypothesis is rejected at the 0.025 level, but is accepted to the 0.01 level. This means that the p-value is between 0.01 and 0.025 b. the p-value of a test is the probability that the null hypothesis is true c. the significance level of a test is the probability that the null hypothesis is true d. all of the above are true statements e. none of the above are true statements 15. With one-tailed tests, there is always a question of which sense of the inequality will be placed in the alternative versus null hypothesis. A useful rule is that the null hypothesis: a. will be held true unless the data contain sufficient contradictory evidence b. is chosen to minimize the cost of type I error c. is chosen to minimize the cost of type II error d. is the one which most people would choose e. none of the above