ECO252 QBA2SECOND HOUR EXAMIn-class materialsNov 8, 2005Exhibit 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 testANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: McNemar test, assumptionIn Method D6b, the McNemar Test, we compare two proportions taken from the same sample. Assume that two different questions are asked of the same group with the following responses.2221121121xxxxnoyesnoyesquestionquestion In this case 1471379321notgoodnotgoodquestionquestion If we wish to test 211210:H:Hpppp,where 1pis the proportion saying ‘yes’ before and 2p is the proportion saying ‘yes’ after, let 2717.33923.1034108347137713721122112xxxxz (The test is valid only if 102112 xx.) 2. Referring to Exhibit 1, what is the null hypothesis?. 3. Referring to Exhibit 1, what is the value of the test statistic using a 1% level of significance?ANSWER:13.37 or 3.37TYPE: PR DIFFICULTY: ModerateKEYWORD: McNemar test, test statistic4. Referring to Table Exhibit 1, what is the p-value of the test statistic using a 5% level of significance?ANSWER:0.0008TYPE: PR DIFFICULTY: ModerateKEYWORD: McNemar test, p-value5. Referring to Table 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.ANSWER:cTYPE: TF DIFFICULTY: ModerateKEYWORD: McNemar test, conclusionExhibit 2 (Problem D7)In 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 that these are independent samples from population with a Normal distribution and that 2221Assume these are paired samples from a Normal distribution.6. Referring to Exhibit 1, what should be the degrees of freedom for this test? a)4DFb)8DFc)9DF2d) 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)7. Referring to Exhibit 1, 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 signedrank test.e) The standard error is irrelevant because we are using a (Mann-Whitney-) Wilcoxon signedrank test.f) We do not have enough information to answer this question. (You must explain what information is missing)8. Referring to Exhibit 1, assume that the correct alternate hypothesis is 21, that use of the formula ddsxxsDdt21210 is correct, that 263.2tand that we there are 27 degrees of freedom (Assume that all of these are correct, even though it is very unlikely!), we should do the following. Note 052.227025.tand 473.22701.tso that the p-value is between .05 and .02. a) Reject the null hypothesis only if the significance level is a value below .01b) Reject the null hypothesis if the significance level is any value below .02c) 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 only if the significance level is above .10f) None of the above.9. Referring to Exhibit 1, assume that the correct alternate hypothesis is 21, that use of the formula ddsxxsDdt21210 is correct, that 877.1tand that there are 273degrees of freedom (Assume that all of these are correct, even though it is very unlikely!), we should do the following. Note 703.12705.tand 052.227025.t, so that the pvalue is between .10 and .05 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.10. You are having a part produced in two different machines. 1x is 201 randomly selected data points that represent
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