252x0621 11 08 06 Page layout view ECO252 QBA2 SECOND HOUR EXAM November 8 2006 Name corrected Circle Hour of Class Registered MWF2 MWF3 TR12 30 TR2 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 20 9 If you are not using the supplement table make sure that I know it 1 P 10 x 35 2 P x 3 3 P 0 x 20 00 4 x 055 252x0621 11 08 06 II 22 points Do all the following 2points each unless noted otherwise Look them over first The exam is normed on 50 points The computer problem is at the end 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 1 A company gives an exam to graduates of quality control programs in two plants samples of scores are as follows Boston 90 73 78 82 66 Atlanta 81 72 50 66 55 70 a Compute the sample variance for Boston Show your work The sample mean and standard deviation for Atlanta are 65 67 and 11 43 2 b Is there a significant difference between the scores in the two plants You may assume that variances are equal State your hypotheses 2 2 252x0621 11 08 06 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 A random sample of 215 potential students who have not taken the orientation is compared with a random sample of 215 students who have taken the orientation Of the first group 130 students viewed the program as good Of group that had taken the orientation 164 viewed the program as good She wishes to see if the fraction that considered the program good has risen because of the orientation 2 Referring to Exhibit 1 which test should she use 2 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 3 Referring to Exhibit 1 what is the null hypothesis 2 4 Referring to Exhibit 1 what is the value of the computed test statistic 4 5 Referring to Table Exhibit 1 what is the p value of the test statistic 2 14 12 3 252x0621 11 08 06 Exhibit 2 Dummeldinger A researcher took a random sample of n graduates of MBA programs which included n1 women and n 2 men Their starting salaries were recorded Use 1 and or 1 for population parameters for women and 2 and or 2 for men 10 The sample yields following data x1 48266 70 x 2 50100 00 n1 n 2 150 The researcher wants to show that men s1 13577 63 s 2 11741 25 have a higher mean starting salary than women Assume that these are independent samples Hint To preserve both our sanity move the decimal point three places to the right in both the means and standard deviations You will be working in thousands but will get the same value for the test ratio and 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 6 Referring to Exhibit 2 if D 1 2 what is the null hypothesis 1 a D 0 b D 0 c D 0 d D 0 e D 0 f None of the above Give the correct one 7 Referring to Exhibit 2 if we do not have a computer available which of the following methods would be most practical and correct for you to use 2 a z test comparing two means b t test comparing two means assuming equal variances c t test comparing two means not assuming equal variances d t test comparing two means for paired data e z test comparing two proportions f None of the above Give the correct one 17 8 Referring to Exhibit 2 assume that the correct alternate formula for a critical value is d cv D0 t 2 s d where t can be replaced by z for one method What is the value of sd 3 20 9 Referring to Exhibit 2 and the previous problems what is the value of the test ratio that we would use to test your hypothesis 2 10 Referring to Exhibit 2 and the previous problems assuming that your null hypothesis is correct do you reject the null hypothesis Why 2 24 11 Extra credit compute a two sided confidence interval for the ratio of the two variances in the previous problem 3 4 252x0621 11 08 06 Exhibit 3 You drive a New York avenue with 25 traffic lights on it You suspect that this is equivalent to playing a game where the probability of success getting a red light is 50 There are 25 tries You use a binomial table p 5 n 25 to figure out the probabilities of getting various numbers of red lights on a single run and then you record the number of times you get these numbers of red lights during 25 trips up the avenue The left column is copied from my cumulative binomial table The next column comes from differencing the first column The third column is the second column multiplied by 25 The fourth column gives the numbers actually observed The last two columns show the process of making the observed data into a cumulative distribution E P x 9 0 11476 120 P x 10 0 21218 280 P x 11 0 34502 400 P x 12 0 50000 480 P x 13 0 65498 600 P x 14 0 78782 720 P x 15 0 88524 880 P x 25 1 00000 1 00 O Cum O Cum O P x 9 0 11476 2 8690 3 3 P x 10 0 09742 2 4355 4 7 P x 11 0 13284 3 3210 3 10 P x 12 0 15498 3 8745 2 12 P x 13 0 15498 3 8745 3 15 P x 14 0 13284 3 3210 3 18 P x 15 0 09742 2 4355 4 22 P x 16 0 11476 2 8690 3 25 12 Referring to Exhibit 3 The correct way to test for the distribution cited is 2 a Kolmogorov Smirnoff Test b Lilliefors Test c Chi squared …
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