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WCU ECO 252 - ECO 252 Second Hour Exam

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252x0621 11/08/06 (Page layout view!) ECO252 QBA2 Name corrected SECOND HOUR EXAM Circle Hour of Class Registered November 8, 2006 MWF2, MWF3, TR12:30, TR2Show 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! 9,20~ Nx - If you are not using the supplement table, make sure that I know it.1.  3510 xP 2.  3xP3.  00.200 xP4. 055.x252x0621 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.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)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.5. Read problems carefully. A problem that looks like a problem on another exam may be quite different.252x0621 11/08/06 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. 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)a)2c-test for difference in proportionsb) z-test for difference in proportionsc) McNemar test for difference in proportionsd) Wilcoxon rank sum test3. 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) [12]5. Referring to Table Exhibit 1, what is the p-value of the test statistic? (2)[14]3252x0621 11/08/06 Exhibit 2 (Dummeldinger) A researcher took a random sample of n graduates of MBA programs, which included1nwomen and 2n 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.63.1357770.4826611sx and 25.1174100.5010022sx. 15021nn. The researcher wants to show that men 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.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 that2221.6. Referring to Exhibit 2, if 21Dwhat is the null hypothesis? (1) a)0Db)0Dc)0Dd)0De)0D 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 meansb) t- test comparing two means assuming equal variancesc) t- test comparing two means not assuming equal variancesd) t- test comparing two means for paired datae) z- test comparing two proportionsf) None of the above . (Give the correct one!) [17]8. Referring to Exhibit 2, assume that the correct alternate formula for a critical value isdcvstDd20, where t can be replaced by z for one method. What is the value of ds? (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)4252x0621 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  25,5.  npto 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 columngives the numbers actually observed. The last two columns show the process of making the observed data into a cumulative distribution. E O Cum O CumnO  9xP0.11476  9xP0.11476 2.8690 3 3.120  10xP0.21218  10xP0.09742 2.4355 4 7.280  11xP0.34502  11xP0.13284 3.3210 3 10.400  12xP0.50000  12xP0.15498 3.8745 2 12.480  13xP0.65498  13xP0.15498 3.8745 3 15.600  14xP0.78782  14xP0.13284 3.3210 3 18.720  15xP0.88524  15xP0.09742 2.4355 4 22.880  25xP1.00000  16xP0.11476 2.8690 3 251.0012. Referring to Exhibit 3. The correct way to test for the distribution cited is: (2) a) Kolmogorov-Smirnoff Testb) Lilliefors Testc) Chi-squared test with 8 degrees of freedomd)


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