1 BUEC 333 Summer 1997 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 17 multiple choice questions, with a value of 5 points each, for a total of 85 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 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. Infinite populations are assumed in all questions where population size is relevant. 1. In brief, hypothesis testing is essentially: a. using sample data in order to make a decision concerning a parameter of the population b. performing a probability test in order to determine whether an assumption appears to be valid c. the assessment of the probability of obtaining observed results under a certain assumption d. constructing numerical limits within which a statistical value is likely to occur, given a specified assumption is true e. all of the above 2. If independent random samples each of size n=200 are drawn from populations that have standard deviations å1 = 30 and å2 = 40, the standard deviation of the sampling distribution of (þ1 - þ2) is: a. 0.35 b. 0.59 c. 10.63 d. 3.54 e. 12.50 3. A market researcher wishes to test whether the proportion of persons who purchase a product after seeing an advertisement differs between two advertisments. Independent random samples are taken, with n1 = 50 and n2 = 100. If 26 persons in the first sample subsequently purchased the product, and 40 persons in the second sample subsequently purchased the product, what is the estimate of the common value of p at p1 = p2? a. 0.52 b. 0.46 c. 0.92 d. 0.50 e. 0.44 4. Two populations are known to be Normally distributed, and it is believed they have equal variances. Independent samples are drawn, with the results: n1 = 10 þ1 = 85.0 s12 = 100.0 n2 = 16 þ2 = 70.0 s22 = 156.0 To test Ho: æ1 = æ2, one needs an estimate of the common variance, å2 (sometimes called the pooled estimate). For this situation, this estimate is: 2 a. 11.6 b. 19.0 c. 20.7 d. 135.0 e. 172.0 5. In a random sample of 500 Accura car owners, the following was the frequency distribution of owners with respect to their occupations: i Occupation fi 1 Professional 160 2 Managerial 195 3 Skilled Trades 75 4 Other 70 In testing whether these data follow a multinomial distribution with p1 = 0.3, p2 = 0.4, p3 = 0.15 and p4 = 0.15 at the à = .05 level, the critical value for the test statistic, against which the calculated value will be compared, is: a. 1.96 b. 6.25 c. 3.84 d. 7.81 e. 1.645 6. Testing Ho: å12 ó å22 against HA: å12 > å22 at the à = .05 level, one should: a. put the larger S2 in the numerator, and reject if the result exceeds the tabled F.10 b. put the larger S2 in the numerator, and reject if the result exceeds the tabled F.05 c. calculate S22/S12 and reject if the result exceeds the tabled F.05 d. calculate S12/S22 and reject if the result exceeds the tabled F.10 e. calculate S12/S22 and reject if the result exceeds the tabled F.05 7. In a study of weight gain by feeder cattle fed on two different feed rations, the results were: Ration 1: 48 55 56 64 Ration 2: 52 56 61 63 68 Using the Mann-Whitney test to see if mean weight gain differs between rations, the calculated value of the test statistic, U, (using the smaller sample) is: a. 10.0 b. 13.5 c. 16.5 d. 28.5 e. 45.0 8. The owner of a boutique wishes to test the hypothesis that 20 per cent of her customers use INTERAC. If n = 250 and the test is conducted at the à = .01 level, the critical values for p-hat are: a. .743 and .857 b. .129 and .271 c. .135 and .265 d. .150 and .250 e. .141 and .259 3 9. If a choice can legitmately be made between a two-tailed parametric test and a nonparametric test (the assumptions for both are satisfied) which test should be conducted? a. the parametric test, because this reduces the probability of Type II error b. the parametric test, because this reduces the probability of Type I error c. the nonparametric test, because this reduces the probability of Type II error d. the nonparametric test, because this reduces the probability of Type I error e. it doesn't matter; both will give the same result 10. The accounts of a company show that on average, accounts receivable are $194.37. A suspicious auditor checks a random sample of 250 of these accounts, finding a sample mean of $187.88 and standard deviation $52.36. What is the lowest level of significance at which the null hypothesis that the population mean is $194.37 can be rejected against a two-sided alternative (i.e., what is the p-value)? a. .05 b. .10 c. .01 d. .025 e. cannot be calculated exactly, over 50% 11. Given the following differences calculated from matched data: d = -4.3, 3.1, 1.5, -5.2, 2.7, 6.5 The calculated test statistic, T, for the Wilcoxon test is: a. 5 b. 6 c. 7 d. 8 e. 9 12. The alternatives in a statistical test are Ho: æ ó 40 and HA: æ > 40. The test is to be conducted with a random sample of n = 81 items generated by a process with known standard deviation å = 18. The following decision rule has been selected: If þ ó 42.5 conclude Ho; if þ > 42.5 conclude HA. The probability of Type II error (á) at æ = 41 is: a. less than 0.5 b. 0.53 c. 0.77 d. zero e. á is not defined for this problem 13. A consumer group surveyed a random sample of 1,000 households which had borrowed money in the past year. The bivariate sampling distribution classified by source of funds and size of loan is: Size of loan Source < $25,000 $25,000-$50,000 Over $50,000 Bank 70 175 25 Credit Union 45 250 70 Other 35 175 155 Testing whether source of funds and size of loan are statistically independent, the expected frequency for the class "Credit Union, $25,000-$50,000" is: 4 a. 54.8 b. 162.0 c. 219.0 d. 250.0 e. 262.0 14. Using a sample of size n = 8000 it is desired to test whether the logarithm of income is distributed Normally, using à = 0.01. Assume the calculated value of the Bowman- Shelton statistic, B, is 9.12. The appropriate conclusion is: a. reject the null hypothesis since 9.12 < 9.21 b. accept the null hypothesis since 9.12 < 9.21 c. accept the null hypothesis since 9.12 < 135.8 d. reject the null hypothesis since 9.12 > 5.46 e. accept the null hypothesis since 9.12 < 118.5 15. Assume the following 20 numbers are IQ scores: 90, 102, 105, 109, 110, 111, 112, 113, 115, 115, 116, 117, 118, 120, 122, 125, 126, 129, 131, 134. The mean of this sample is 116 and the standard deviation is 10.48. Using a Chi- square test for distribution shape to test for Normality (four classes each with expected frequencies = 5), you will want 25% of the area in each of 4 classes. The observed frequency for the first (lowest IQ scores) class is: a. 2 b. 3 c. 4 d. 5 e. 6 16. A machine produces a particular type of part which should have diameters Normally distributed with variance å2 = 1 cm if the machine is properly adjusted. A random sample of 20 parts yielded þ = 6.8 cm and s = 0.7 cm. Testing whether the machine is properly adjusted yields the test statistic: a. 1.43 b. 2.04 c. 9.31 d. 13.3 e. 30.14 17. Suppose it is desired to test whether the population median is equal to 25.0, using the sign test. In this situation, the exact sampling distribution of the test statistic is: a. normal b. binomial c. exponential d. chi-square e. none of the above