1BUEC 333 Summer 2000 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. Questions 1 - 4 refer to the following information. A retail store sells two products, AAA and ZZZ. The following table gives data on sales of each product and number of customers for a 30 day period (n=30): Customers Sales of AAA Sales of ZZZ Sample mean 47.4 1.633 1.233 Sample std. dev. 32.054 1.377 1.591 1. It is desired to test whether the number of units of AAA sold per day averages more than 1.5. At the 5% level, what is the critical value (limit of the acceptance region)? a. 1.914 b. 1.927 c. 1.934 d. 2.060 e. 3.840 2. Suppose it was decided that sales of each item in a day probably depended on the number of customers who came into the store that day. How could this be taken into account when trying to determine whether AAA sales differed from ZZZ sales? a. That dependence is already accounted for in a difference of means test. b. Use a paired differences test. c. Use a Mann-Whitney test. d. Use a Chi-square test. e. That dependence cannot be accounted for statistically with any test in chapters 9-11. 3. To test the hypothesis that the number of AAA sold per day is the same as the number of ZZZ sold per day, what is the pooled estimate of the variance? a. 1.484 b. 1.488 c. 1.896 d. 2.213 e. 2.531 4. Testing the null hypothesis that the average number of customers per day is greater than or equal to 50, what is the p-value for this test? a. Between 5 and 10 per cent b. Between 2.5 and 5 per cent c. Between 1 and 2.5 per cent d. Cannot be determined without knowing alpha. e. None of the above. 5. A random sample of 100 adults was asked to rate two movies on a scale of 1-100. Fifty people preferred the action movie, 40 people preferred the comedy and 10 people rated them both the same. Testing the hypothesis that half of the population prefers action movies, the calculated test statistic is: a. zero b. 0.61 c. 1.05 d. 1.11 e. 1.63 6. It is desired to test whether the distribution of the number of typographical errors per page is Poisson distributed. If lambda=0.3, what is the expected number of error-free pages in a sample of 250 pages? a. 64.80 b. 74.08 c. 175.00 d. 185.20 e. 196.66 7. Consider the following three statements: (i) The significance level of a test is the probability that the null hypothesis is false. (ii) If a null hypothesis is rejected at the 0.025 level, then it must be rejected at the 0.01 level. (iii) The p-value of a test is the probability that the null hypothesis is true. a. All three statements are true. b. (i) and (ii) are true, but (iii) is false. c. (i) and (ii) are false, but (iii) is true. d. (i) and (iii) are false, but (ii) is true. e. All three statements are false. 8. In testing the null hypothesis that the population proportion is greater than or equal to 0.5 with a sample of n=400, it is decided to reject the null hypothesis if the sample proportion is less than 0.45. Then if the true proportion is 0.4, beta: a. Cannot be determined without knowing alpha. b. Cannot be determined without knowing the sample proportion. c. Is less than 50% d. Is more than 90% e. Is zero 9. In order to use the Wilcoxon test, we must have: a. Independent samples b. Normality c. Large samples d. Symmetry e. Equal variances 10. In a multinomial population with three attribute categories, A, B, and C; it is hypothesized that p(B)=0.5 and p(C)=0.2. If a random sample of size n=30 is selected, yielding 10 items with each attribute, what is the calculated Chi-square for testing the goodness of fit hypothesis? a. 4.44 b. 4.20 c. 3.84 d. 1.28 e. 1.00 Questions 11 and 12 refer to the following information. A manufacturer has two machines which produce bolts, a new machine that in a sample of size n=64 yielded a mean of 5 cm and a standard deviation of 0.18 cm; and an old machine which in a sample of size n=49 yielded a mean of 5.2 with a standard deviation of 0.07. 11. Testing whether the variance of the new machine is greater than the acceptable variance of 0.03, the calculated test statistic is: a. 69.12 b. 68.04 c. 57.60 d. 56.70 e. 51.84 12. Testing whether the variances of the two machines are equal the calculated test statistic is: a. 6.61 b. 3.38 c. 2.57 d. 1.31 e. 0.96 13. Using a Mann-Whitney test to test whether two means are equal with both samples of size n=10, if the sum of the ranks for one sample is 120: a. the sum of ranks for the other sample must be 100 b. the value of the U statistic is 40 c. the mean of the U statistic is 55 d. the variance of the U statistic is indeterminate e. none of the above 14. In a Chi-square test for independence with 4 rows and 3 columns, one cell is found to have an expected frequency less than 5. After correcting for this, the degrees of freedom are: a. 4 b. 3 c. either 3 or 4 depending on the correction d. 5 e. none of the above 15. Consider the following three statements: (i) In order to simulteneously reduce alpha and beta, the sample size must be increased (ii) In testing hypotheses, the variance must be calculated under the assumption that the null hypothesis is true (iii) Testing whether two proportions are equal can be done either with the Normal or the Chi-square a. All three statements are true. b. (i) and (ii) are true, but (iii) is false. c. (i) and (ii) are false, but (iii) is true. d. (i) and (iii) are false, but (ii) is true. e. All three statements are false.