BUEC 333 Summer 2003 D. Maki MIDTERM EXAMINATION - A Important - Ensure that the letter "A", "B" or "C" from the examination title above matches the one recorded on the top front of your answer sheet in red. This examination consists of 15 multiple choice questions, equally weighted. 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 = 1 hour and 50 minutes. Infinite populations are assumed in all questions where population size is relevant. 1. In a period of 100 minutes, there were a total of 190 arrivals at a highway toll booth. The table below shows the frequency of arrivals per minute over this period. Testing the null hypothesis that the distribution is Poisson, the expected frequency for the "4 or more arrivals" class is: Number of arrivals in minutes 0 1 2 3 4 or more Observed Frequency 10 26 35 24 5 a. 5 b. 14.96 c. 12.53 d. less than 5 e. not calculable - open ended class 2. In selecting between the alternative H0: mu less than or equal to 100 and HA: mu greater than 100, the following decision rule is to be employed: If X-bar is less than or equal to 120, accept H0; otherwise accept HA:. Further, the probability of accepting HA: at mu=100 is 0.08. The alpha risk at mu=90 is: a. positive, but less than 0.08 b. equal to 0.08 c. greater than 0.50 d. zero e. none of the above 3. Seventy percent of the customers of a certain store are women. A random sample of n=2 customers is selected. The sampling distribution of p-hat, the proportion of women in the sample is: a. p-hat 0 .5 1.0 Prob(p-hat) .09 .42 .49 b. p-hat 0 .5 1.0 Prob(p-hat) 1/3 1/3 1/3 c. p-hat 0 1.0 Prob(p-hat) .3 .7 d. Normal with mean = E(p-hat) = .7 and Var(p-hat) = .105 e. none of the above 4. Testing H0: Sigma-squared less than or equal to 5 against HA: Sigma-squared greater than 5, at the alpha = .05 level with a sample of n=10, what is beta, the probability of type II error, if the true sigma=squared is 20.3? a. zero b. 10% c. 50% d. over 50% e. beta is not defined for tests like this 5. Some retail salespeople are classified by years of experince and average monthly sales in the following table. Average Sales Experience <$5,000 $5,000-$10,000 Over $10,000 < one year 9 8 3 1-5 year 10 33 7 > 5 years 3 7 10 After all combinations required to make the Chi-square approximation valid have been made, how many degrees of freedom are there for a test of independence between sales and experience? a. 2 b. 3 c. 4 d. 8 e. none of the above Questions 6, 7 and 8 refer to the following problem setting: Five salespersons were required to take a one-day short course on improving their sales techniques. Their sales for the month before the course and the month after the course are shown below. Person Sales Before Sales After A $4,200 $4,500 B 3,500 3,700 C 5,100 5,000 D 2,600 2,700 E 3,300 3,300 6. Testing the null hypothesis that sales did not improve using a parametric test at the alpha=0.1 level yields the conclusion:. a. accept H0: since 0.63 < 1.638 b. accept H0: since 0.63 < 1.533 c. accept H0: since 1.41 < 1.533 d. reject H0: e. none of the above 7. Testing the null hypothesis that sales did not improve using the sign test yields the p-value: a. over 0.5 b. 0.1874 c. 0.2500 d. 0.3125 e. none of the above 8. Testing the null hypothesis that sales did not improve using the Wilcoxon test at the alpha=0.1 level yields the conclusion: a. reject H0: since 1.5 > 1 b. accept H0: since 1.5 > 1 c. reject H0: since 1.5 < 3 d. accept H0: since 1.5 < 3 e. none of the above 9. Testing the null hypothesis that two means are equal against the alternative that they are not equal, the following information is available. For the first sample the mean is 65, the sample estimate of the variance is 90, and the sample size is 11. For the second sample, independent of the first, the mean is 72, the sample estimate of the variance is 100, and the sample size is again 11. The conclusion is: a. accept the null hypothesis at any alpha less than 0.2 b. reject the null hypothesis at any alpha less than 0.2 c. reject the null hypothesis at alpha=.1 d. reject the null hypothesis at alpha=0.2 but accept at alpha=.1 e. none of the above 10. The interest rates paid by a sample of banks on a given day were: 3, 3.25, 3.5, 4. On the same type of account, the interest rates paid by an independent sample of credit unions on the same day were: 3.75, 3.75, 4, 4.5, 4.7. Testing whether the mean rates for banks and credit unions were the same using an appropriate nonparametric test, the result is: a. the p-value is less than .05 b. the p-value is .0658 c. the p-value is .0718 d. the p-value is .0892 e. the p-value is greater than .10 11. We test H0: mu less than or equal to 100 against HA: mu greater than 100. We decide to reject H0: for any X-bar greater than or equal to 110. In our sample, X-bar turns out to be 110. Then, if the true mean is 105, beta, the probability of type II error, is: a. greater than 50% b. exactly 50% c. greater than alpha but less than 50% d. less than alpha e. without knowing sigma and n, we know nothing about beta 12. Testing the null hypothesis that the variance of population A is greater than or equal to the variance of population B, we calculate an F ratio by: a. putting the larger sample variance in the numerator b. putting the sample variance for the larger sample in the numerator c. always putting the variance from sample A in the numerator d. putting the variance from sample A in the numerator if the samples are of equal size e. none of the above 13. It is desired to test whether two sample proportions are equal. The first sample yields 150 successes out of 180 trials, while the second sample yields 75 successes out of 100 trials. Using a Normal approximation, the conclusion is: a. the p-value is less than .05 b. the p-value is greater than .10 but less than .15 c. the p-value is greater than .05 but less than .10 d. the p-value is greater than .15 but less than .20 e. none of the above 14. Testing the null hypothesis that the proportion of drivers who exceed the speed limit on a certain stretch of highway is 0.7 against a two-tailed alternative at the alpha=.05 level, a sample of size n=10 detects 6 speeders. The decision rule is to reject H0: if: a. either 9 or more or 5 or less speeders are detected b. either 10 or 4 or less speeders are detected c. either 9 or more or 4 or less speeders are detected d. either 9 or more or 3 or less speeders are detected e. either 10 or 3 or less speeders are detected 15. A financial analyst has calculated the percent rate of return earned by investors in 2001 on each of a random sample of 25 corporate bonds. The sample mean and standard deviation are x-bar=8.0 and S=1.5, respectively. She wishes to test whether the distribution is normally distributed, using a chi-square test of goodness of fit with 5 classes of equal expected frequency. The largest class (i.e. the class to which the largest rates of return will be assigned) is: a. 8.38 and above b. 9.92 and above c. 8.25 and above d. 9.26 and above e. none of the above