252x0562 11/09/05 (Page layout view!) ECO252 QBA2 Name Key SECOND HOUR EXAM Circle Hour of Class Registered November 9, 2005 MWF2, MWF3, TR12:30, TR3 Show 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! 6,23~ Nx - If you are not using the supplement table, make sure that I know it.1. 30xP2. 3000.2 xP3. 00.230 xP 4. 055.x252x0562 11/09/05 (Page layout view!) II. (24+ points) Do all the following? (2points each unless noted otherwise).Exhibit 1The director of the MBA program of a state university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good. Given below is the result from 215 students’ view of the program before and after the orientation.After the OrientationBefore the Orientation Good Not Good TotalGood 93 37 130Not Good 71 14 85Total 164 51 2151. Referring to Exhibit 1, which test should she use?a)2c-test for difference in proportionsb) Z-test for difference in proportionsc) McNemar test for difference in proportionsd) Wilcoxon rank sum test2. Referring to Exhibit 1, what is the null hypothesis?. 3. Referring to Exhibit 1, what is the value of the computed test statistic ?4. Referring to Exhibit 1, what should be the director’s conclusion? 04.a) There is sufficient evidence that the proportion of potential incoming students who perceive the program as being good is the same before and after the orientation.b) There is insufficient evidence that the proportion of potential incoming students who perceive the program as being good is the same before and after the orientation.c) There is sufficient evidence that the proportion of potential incoming students who perceive the program as being good is not the same before and after the orientation.d) There is insufficient evidence that the proportion of potential incoming students who perceive the program as being good is not the same before and after the orientation.2Note 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.252x0562 11/09/05 (Page layout view!)Exhibit 2 Note that problems 5, 6 and 7(!!!!) are based on exhibit 2In a study of sleep gotten with a sleeping pill and with a placebo the results were (Keller, Warren, Bartel,2nd ed. p. 354) 1x 2x d Pill Placebo difference 7.3 6.8 .5 8.5 7.9 .6 6.4 6.0 .4 9.0 8.4 .6 6.9 6.5 .4197.1620.7211sx 997.0120.7222sx 010.0500.02dsdWe want to see if the means or medians, as appropriate, are different. Assume these are paired samples from a Normal distribution.5. Referring to Exhibit 2, what should be the degrees of freedom for this test? a)4DFb)8DFc)9DFd) 9341.741994.042394.04388.01122222222121212222121nnsnnsnsnsDF(Rounded to 7.)e) Degrees of freedom are irrelevant because we are using a (Mann-Whitney-) Wilcoxon rank sum test.f) Degrees of freedom are irrelevant because we are using a Wilcoxon signed rank test.g) We do not have enough information to answer this question. (You must explain what information is missing)6. Referring to Exhibit 2, in the formula dstdD2, we should use the following. a)447.0002.5010.0nssddb)6624.04388.0222121nsnssdc) 097.18947.04197.14211ˆ212222112nnsnsnsp, which is used to compute 662.0439.05151097.111ˆ21nnsspdd) The standard error is irrelevant because we are using a (Mann-Whitney-) Wilcoxon ranktest.e) The standard error is irrelevant because we are using a Wilcoxon signed rank test.f) We do not have enough information to answer this question. (You must explain what information is missing)3252x0562 11/09/05 (Page layout view!)7. Referring to Exhibit 2, assume that the correct alternate hypothesis is 21, that use of the formula ddsxxsDdt21210 is correct, that 877.1tand that there are 27 degrees of freedom (Assume that all of these are correct, even though it is very unlikely!), we should do the following. a) Reject the null hypothesis only if the significance level is a value below .025b) Reject the null hypothesis if the significance level is any value below .025c) Reject the null hypothesis if the significance level is any value above .025d) Reject the null hypothesis if the significance is any value above .05e) Reject the null hypothesis if the significance level is any value above .10f) None of the above.8. You are having a part produced in two different machines. 1x is 101 randomly selected data points that represent the length of parts from machine one, 2x is 126 randomly selected data points that represent the length of parts from machine two. You want to test your suspicion that parts from machine one are more variable in length than parts from machine two (This is the same as saying that machine 2 is more reliable than machine 1). Test this suspicion after stating your hypotheses. Your sample means are 25.593 inches for machine 1 and 25.592 for machine 2. Sample standard deviations are 8.379 for machine 1 and 6.964 for machine 2.9. (Extra credit) compute a confidence interval for the ratio of the two variances in the previous problem.4252x0562 11/09/05 (Page layout view!)10. The following problem is an easier version of a problem in the text.A pet food canning factory produces 8 oz cans of cat food. The manager suspects that the amount of cat food put into the cans by machine 2 is significantly larger than that put in by machine 1. A sample of output is taken with the results below. 012.81x
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