ECO252 QBA2 SECOND HOUR EXAM In class materials Nov 8 2005 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 1 After the Orientation Good Not Good 93 37 71 14 164 51 Total 130 85 215 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 ANSWER c TYPE MC DIFFICULTY Moderate KEYWORDS McNemar test assumption In 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 question 1 yes no question 2 question 1 yes no In this case good x11 x12 x not 21 x 22 If we wish to test H 0 p1 p 2 where H1 p1 p 2 proportion saying yes after let z question 2 good not 93 37 71 14 p1 is the proportion saying yes before and p 2 is the x12 x 21 x12 x 21 37 71 37 71 34 34 3 2717 The 10 3923 108 test is valid only if x12 x 21 10 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 1 3 37 or 3 37 TYPE PR DIFFICULTY Moderate KEYWORD McNemar test test statistic 4 Referring to Table Exhibit 1 what is the p value of the test statistic using a 5 level of significance ANSWER 0 0008 TYPE PR DIFFICULTY Moderate KEYWORD McNemar test p value 5 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 c TYPE TF DIFFICULTY Moderate KEYWORD McNemar test conclusion Exhibit 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 x1 x2 d Pill 7 3 8 5 6 4 9 0 6 9 x1 7 620 Placebo 6 8 7 9 6 0 8 4 6 5 x 2 7 120 d 0 500 s12 s 22 s d2 0 010 1 197 0 997 difference 5 6 4 6 4 We 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 12 22 Assume these are paired samples from a Normal distribution 6 Referring to Exhibit 1 what should be the degrees of freedom for this test a DF 4 b DF 8 c DF 9 2 d DF s12 s 22 n1 n 2 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 e 7 Referring to Exhibit 1 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 signed rank test e The standard error is irrelevant because we are using a Mann Whitney Wilcoxon signed rank 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 1 2 that use of the are 27 formula t d D 0 x1 x 2 1 2 is correct that t 2 263 and that we there sd sd degrees of freedom Assume that all of these are correct even though it is very unlikely we should do the following 27 27 Note t 025 2 052 and t 01 2 473 so that the p value is between 05 and 02 a Reject the null hypothesis only if the significance level is a value below 01 b Reject the null hypothesis if the significance level is any value below 02 c Reject the null hypothesis if the significance level is any value above 025 d Reject the null hypothesis if the significance is any value above 05 e Reject the null hypothesis only if the significance level is above 10 f None of the above 9 Referring to Exhibit 1 assume that the correct alternate hypothesis is 1 2 that use of the formula t d D 0 x1 x 2 1 2 is correct that t 1 877 and that there are 27 sd sd 3 degrees of freedom Assume that all of these are correct even though it is very unlikely we should do the following 27 27 Note t 05 1 703 and t 025 2 052 so that the pvalue is between 10 and 05 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 10 You are having a part produced in two different machines x1 is 201 randomly selected data points that represent the length of parts from machine one x 2 is 501 randomly selected data points that represent the length of parts from machine two You want to test your suspicion that …
View Full Document
Unlocking...