252x0721 3/19/07 ECO252 QBA2 Name SECOND HOUR EXAMMarch 23 2007Show your work! Make Diagrams! Exam is normed on 50 points. Answers without reasons are not usually acceptable.I. (8 points) Do all the following. Make diagrams! 7,10~ Nx - If you are not using the supplement table, make sure that I know it.1. 257 xP 2. 15xP3. 05 xP4. 085.x (Do not try to use the t table to get this.)1252x0721 3/19/07 II. (22+ points) Do all the following? (2points each unless noted otherwise). Look them over first – the computer problem is at the end. Show your work where appropriate.Note the following:1. This test is normed on 50 points, but there are more points possible including the take-home. You are unlikely to finish the exam and might want to skip some questions.2. A table identifying methods for comparing 2 samples is at the end of the exam.3. If you answer ‘None of the above’ in any question, you should provide an alternative answer and explain why. You may receive credit for this even if you are wrong.4. Use a 5% significance level unless the question says otherwise.5. Read problems carefully. A problem that looks like a problem on another exam may be quite different. 6. Make sure that you state your null and alternative hypothesis, that I know what method you are using and what the conclusion is when you do a statistical test.1. (Anderson, Sweeny, Williams) We wish to compare miles per gallon of two similar automobiles. A random sample of 8 automobiles is chosen and 8 drivers are asked to drive the cars on identical roads. The data is as follows.Row Driver Model 1 Model 2 difference 1x 2x d 1 1 28 26 2 2 2 23 22 1 3 3 25 27 -2 4 4 23 22 1 5 5 24 23 1 6 6 26 25 1 7 7 29 27 2 8 8 24 26 -2I have computed 25.251x, 2520.21s, 75.242x and 1213.22sa. Compute the sample variance for the d column – Show your work! (2)b. Is there a significant difference between the gas consumption in the two models? State your hypotheses! (2)c. Test to see if the variances of the two cars’ gas consumption are similar. (2) [6]2252x0721 3/19/07Exhibit 1: A quality control engineer is in charge of manufacture of computer disks. Two different processes can be used to manufacture the disks. The engineer suspects that the Kohler method produces a greater proportion of defective disks than the Russell method. Out of a sample of 150 Kohler disks, 27 are defective. Out of a sample of 200 Russell disks, 18 are defective. If Kohler disks are sample 1 and Russell disks are sample 2, test the engineer’s suspicion at the 1% level. 2. The hypotheses that should be tested in exhibit 1 area. 0:210 ppH and 0:211 ppHb. 0:210 ppH and 0:211 ppHc. 0:210 ppH and 0:211 ppHd. 0:210 ppH and 0:211 ppHe. 0:210 ppH and 0:211 ppHf. 0:210 ppH and 0:211 ppHg. None of the above. (Write in correct answer.) [8]3. For exhibit 1, find the value of the test ratio. (3) [11]4. For exhibit 1, the hypotheses in 2 and the test ratio in 3 draw an approximately normal curve and show the ‘reject’ region by shading it. (3) [14]5. For exhibit 1and the hypotheses in 2, find a p-value for the test. (2) [16]5a.For exhibit 1, find a 17% 17.2-sided confidence interval for the difference between the 2 proportions. (4)3252x0721 3/19/07Exhibit 2: A data entry operation sends a group of its employees to a typing course. The table below showstheir speed before 1x and after 2x. 21xxd . 1r and 2r represent the ranks of the numbers when the before and after speeds are ranked between 1 and 16. d is the absolute value of the items in the d column. dr drops the zero and ranks the numbers in d from 1 to 7 and *dr is the ranks with their signs added.Row Processor Before rB After rA d abs d rank sRank 1x 1r 2x 2r d d dr *dr 1 1 59 5.5 57 3.5 2 2 2.5 2.5 2 2 57 3.5 62 9.0 -5 5 7.0 -7.0 3 3 60 7.5 60 7.5 0 0 * * 4 4 66 12.0 63 10.5 3 3 4.0 4.0 5 5 68 13.0 69 14.0 -1 1 1.0 -1.0 6 6 59 5.5 63 10.5 -4 4 5.5 -5.5 7 7 72 15.0 74 16.0 -2 2 2.5 -2.5 8 8 52 1.0 56 2.0 -4 4 5.5 -5.56. Assume that exhibit 2 represents the scores of one sample of eight employees before and after the training. Can we say that the median speed has risen? Do an appropriate statistical test. (3) [19]7. Assume that instead the before and after columns represent independent samples. Can we say that the median speed has risen? Do an appropriate statistical test. (3) [22]4252x0721 3/19/078. The owner of Mother Truckers (which actually moved me once) wants to prove that her firm is superior to her arch rivals Wallflower Van Lines and wants to use proportion of shipment with claims filed as a way of doing that. She assembles the following data.Mother Truckers WallflowerTotal Shipments Sampled 900 750Total number of shipments with 162 60claims over $50 Which would be proper to analyse the data?a. 2 test for independence.b. 2 test for homogeneityc. ANOVAd. z test for comparing 2 proportions.e. Sign testf. The McNemar Testg. None of the above.9. Which is the closest to the probability that a 2 random variable with 4 degrees of freedom will be greater than 10?a. .01b. .05c. .10d. .99e. .95f. .9010. During a period of 20 days 720 patients arrive at a hospital or an average of 1.5 per hour over 480 hours. For example during 106 of the 480 hours there were no arrivals. See if a Poisson distribution fits these data. (6) [32]Row x O xO 1 0 106 0 2 1 140 140 3 2 125 250 4 3 106 318 5 4 3 12 6 5 or more 0 0 480 720 5252x0721 3/19/0711. Computer question.a. Turn in your first computer output. Only do b, c and d if you did. (3)b. A researcher believes that bank CEOs are paid more than utility CEOs. A random sample of eight salaries (in thousands) is collected for each industry. What were the
View Full Document
Unlocking...