252x0562 11 09 05 Page layout view Registered ECO252 QBA2 SECOND HOUR EXAM November 9 2005 Name Key Circle Hour of Class 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 x N 23 6 If you are not using the supplement table make sure that I know it 1 P x 30 2 P 2 00 x 30 3 P 0 x 23 00 4 x 055 252x0562 11 09 05 Page layout view II 24 points Do all the following 2points each unless noted otherwise 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 Exhibit 1 The 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 Before the Orientation Good Not Good Total After the Orientation Good Not Good 93 37 71 14 164 51 Total 130 85 215 1 Referring to Exhibit 1 which test should she use 2 a c test for difference in proportions b Z test for difference in proportions c McNemar test for difference in proportions d Wilcoxon rank sum test 2 3 Referring to Exhibit 1 what is the null hypothesis 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 Referring to Exhibit 1 what is the value of the computed test statistic 2 252x0562 11 09 05 Page layout view Exhibit 2 Note that problems 5 6 and 7 are based on exhibit 2 In a study of sleep gotten with a sleeping pill and with a placebo the results were Keller Warren Bartel 2nd ed p 354 x1 x2 d Pill 7 3 8 5 6 4 9 0 6 9 x1 7 620 Placebo difference 6 8 5 7 9 6 6 0 4 8 4 6 6 5 4 x 2 7 120 d 0 500 s12 1 197 s 22 0 997 s d2 0 010 We 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 DF 4 b DF 8 c DF 9 s 2 s 2 2 d DF e 1 2 n1 n 2 2 2 s12 s 22 n1 n2 n1 1 n2 1 0 4388 2 0 2394 2 0 1994 2 4 7 9341 Rounded to 7 4 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 D d t 2 sd we should use the following a sd b sd c s 2p sd n 0 010 5 002 0 447 s12 s 22 0 4388 0 6624 n1 n 2 n1 1 s12 n2 1 s22 compute s d s p n1 n2 2 4 1 197 4 0 947 1 097 which is used to 8 1 1 1 1 1 097 0 439 0 662 n1 n 2 5 5 d The standard error is irrelevant because we are using a Mann Whitney Wilcoxon rank test 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 3 252x0562 11 09 05 Page layout view 7 Referring to Exhibit 2 assume that the correct alternate hypothesis is 1 2 that use of the formula t 27 d D 0 x1 x 2 1 2 is correct that t 1 877 and that there are sd sd degrees of freedom Assume that all of these are correct even though it is very unlikely we should do the following a b c d e f Reject the null hypothesis only if the significance level is a value below 025 Reject the null hypothesis if the significance level is any value below 025 Reject the null hypothesis if the significance level is any value above 025 Reject the null hypothesis if the significance is any value above 05 Reject the null hypothesis if the significance level is any value above 10 None of the above 8 You are having a part produced in two different machines x1 is 101 randomly selected data points that represent the length of parts from machine one x 2 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 4 252x0562 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 x1 8 012 x 2 8 020 s1 0 048 s 2 0 015 n1 176 n 2 144 …
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