BUEC 333 Summer 1999 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 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. Questions 1-3 are based on the following: A real estate agent collects data on 32 brick homes and 43 non-brick homes placed on the market in the past year - 22 of the brick homes and 24 of the non-brick homes sold in the first month they were on the market. 1. If the agent's alternative hypothesis is that more than 60% of all brick homes will sell within the first month, what is the p-value for testing this? a. 0.1423 b. 0.1562 c. 0.2846 d. 0.3124 e. greater than 0.5 2. If the agent wished to test whether the proportion of brick and non-brick homes which sell within the first month are equal, what is the estimated standard error of the difference between the two proportions? a. 0.112 b. 0.114 c. 0.056 d. 0.013 e. 0.003 3. Testing the alternative hypothesis that the proportion of brick homes that sell within the first month is greater than the proportion of non-brick homes that sell within the first month, which of the following is an example of a Type II error? a. concluding there is a difference when there is none. b. concluding there is a difference when there is one. c. concluding non-brick sells faster when this is false. d. concluding non-brick sells faster when this is true. e. none of the above. 4. Because t-tables are not as complete as z-tables, it might be tempting to use z-tables to calculate p-values when t-tables should actually be used. This cannot be done because: a. the z-table would consistently underestimate the p-value b. the z-table would consistently overestimate the p-value c. p-values are not important in t-distributions d. the definition of p-values is different for t- and z-distributions e. none of the above 5. Terry Offen wonders whether the amount of time he is late for classes depends on whether he likes the subject or not. With this in mind, Terry collects two samples. For classes he likes, Terry was 6, 10, 9 and 3 minutes late. For classes he doesn't like, Terry was 10 14 and 15 minutes late. For this problem, the pooled variance estimate is: a. 17.6 b. 7.3 c. 6.3 d. 8.8 e. 5.5 6. Linus Driver wants to test whether there is a difference in the populations for the top batting averages in the National and American leagues. To check this, Linus collects the top 20 averages in the two leagues and ranks them. The American league ranks were 5, 7, 8, 11, 12, 13, 14, 15, 17, 18, 19 and 20. Which of the following could be the observed value for the U statistic? a. 48 b. 168 c. 51 d. 159 e. 81 7. A sign test of a two-sided hypothesis regarding the population median yields 7 plus signs out of a sample of size 10. The p-value is: a. .0547 b. .1719 c. .1094 d. .3438 e. impossible to determine without knowing alpha 8. It is desired to test whether the 9 numbers: -2, -1, -1, 0, 0, 0, 1, 1, 2 are drawn from a Normal population. The value of the calculated test statistic is: a. 0.56 b. 1.78 c. 2.25 d. 4.00 e. 64.87 Questions 9 and 10 are based on the following: Two machines manufacture a product with a mean width of 3 cm. In a sample of 25 units produced on a new machine the sample standard deviation of width was 0.18 cm. In a sample of units produced on the old machine the sample standard deviation of width was 0.10 cm. 9. Testing whether the variance of the new machine is greater than the acceptable variance of 0.0144, what is the calculated test statistic? a. 300.00 b. 312.50 c. 56.25 d. 54.00 e. 5.10 10. Testing whether the variances of the two machines are equal yields a calculated test statistic: a. 1.80 b. 3.24 c. 1.00 d. impossible to calculate without more information e. none of the above 11. For a two-tailed test of whether two variances are equal, with 16 observations in the first sample and 25 in the second sample, the critical value for testing at alpha=0.10 is: a. 2.11 b. 2.29 c. 2.89 d. impossible to tell without a 10% table e. impossible to tell without knowing more about the sample results. 12. A researcher is testing for independence of sugar eating habits (4 categories, initially) from number of dental caries per visit to the dentist (3 catgegories, initially). The degrees of freedom for the final test statistic are: a. 12 b. 11 c. 10 d. 6 e. less than or equal to 6 13. In order to control both types of risks in a statistical test for a population mean, we must: a. choose the sample size appropriately b. assume normality c. set either the alpha-risk or the beta-risk to zero d. make sure the alpha-risk and beta-risk sum to unity e. use the Normal distribution rather than the t-distribution. Questions 14 and 15 are based on the following: Five people were used to test the effectiveness of a sleeping pill versus a placebo (one night the pill, one night a week later the placebo). The following gives the hours of sleep: Person Sleeping Pill Placebo Difference 1 7.3 6.8 0.5 2 8.5 7.9 0.6 3 6.4 6.0 0.4 4 9.0 8.4 0.6 5 6.9 6.5 0.4 14. Using a parametric test of the hypothesis that the sleeping pill is effective, the calculated value of the test statistic is: a. 5.00 b. 5.59 c. 11.18 d. 2.50 e. 2.132 15. Using the Wilcoxon test to test the hypothesis that the sleeping pill is effective: a. the test cannot be applied since there are no negative differences b. T = 15 c. the null hypothesis is rejected at any alpha d. the null hypothesis is rejected if alpha is greater than .05 e. the null hypothesis is accepted