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OSU BUSMGT 2320 - Comparisons of Two Populations (mu) Additional Practice

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Comparisons [µ] - Additional Practice Problems (1) If some natural relationship exists between each pair of observations that provides a logical reason to compare the first observation of sample 1 with the first observation of sample 2, the second observation of sample 1 with the second observation of sample 2, and so on, the samples are referred to as: a. matched samples b. independent samples c. weighted samples d. random samples (2) True or False. A researcher is curious about the effect of sleep on students’ test performances. He chooses 50 students and gives each two tests: one given after four hours of sleep and one after eight hours of sleep. The test the researcher should use would be matched pairs t-test. (3) Consider the following hypothesis test: a. What is the appropriate distribution for the test statistic (“Z” or “t”)? If “t”, also indicate the degrees of freedom. b. What are the value(s) of the critical point(s)? Express your answer to 3 decimal places. c. What is the 95% Confidence Interval estimate of µ1  µ2. Express your answer to 3 decimal places. d. “Reject” / “Do not reject” null hypotheses? e. Conclusion? Ho: 1  2 = 1.7 H1: 1  2 ≠ 1.7 n1 = 20 n2 = 35 X1= 25.2 X2= 20.4 s1 = 4 s2 = 7  = 0.05(4) The number of degrees of freedom associated with the t test, when the data are gathered from a matched pairs experiment with 10 pairs, is: a. 10 b. 20 c. 9 d. 18 Use the following narrative to answer questions (5) and (6). Automobile insurance appraisers examine cars that have been involved in accidental collisions to assess the cost of repairs. An insurance executive is concerned that different appraisers produce significantly different assessments. In an experiment 10 cars that have recently been involved in accidents were shown to two appraisers. Each assessed the estimated repair costs. These results are shown below. Car Appraiser 1 Appraiser 2 1 1650 1400 2 360 380 3 640 600 4 1010 920 5 890 930 6 750 650 7 440 410 8 1210 1080 9 520 480 10 690 770 (5) What does D1 equal? a. 1650 – 360, the range of repair cost assessments for Appraiser 1 b. 816, the average repair cost assessment for Appraiser 1 c. 762 – 816, the difference in average repair cost assessments for Appraiser 1 and Appraiser 2 d. 1650 – 1400, the difference in Appraiser 1’s repair cost assessment for car 1 and Appraiser 2’s repair cost assessment for car 1 (6) Can the executive conclude at the 5% significance level that the appraisers differ in their assessments? (7) Two types of new cars, Type A and Type B, are being considered for purchase by a fleet manager for a government agency. An important criterion in the purchase decision is gas mileage. The fleet manager has reason to think that Type A gets better gas mileage (literature, word-of-mouth, etc.), but isn’t convinced. He is able to arrange a test of both types of cars. A random sample of 36 cars of Type A had an average gas mileage of 24 miles per gallon with a standard deviation of 1.5 miles per gallon. A random sample of 36 cars of Type B had an average gas mileage of 22.5 miles per gallon with a standard deviation of 2.0 miles per gallon. Is the difference in the sample averages large enough to “convince” the fleet manager that Group A gets better mileage using a significance level of 5%. (8) The symbol Dx refers to: a. the difference in the means of two dependent populations b. the difference in the means of two independent populations c. the matched pairs differences d. the mean difference in the pairs of observations taken from two dependent samples(9) Consider the following hypothesis test: a. What is the appropriate distribution for the test statistic (“Z” or “t”)? If “t”, also indicate the degrees of freedom. b. What are the value(s) of the critical point(s)? Express your answer to 3 decimal places c. What is the value of the observed statistic? Express your answer to 3 decimal places d. “Reject” / “Do not reject” null hypotheses? e. Conclusion? (10) The Human Resources Department of a company wants to determine if a training program is effective in improving a job skill. The following test score data for six employees who were tested both before and after participating in the training program is collected. Can we conclude that the training program is effective at the 0.05 significance level? Employee Before(1) After(2) Sam 85 94 Tamika 94 92 Brian 78 79 Mike 87 88 Mary 74 80 Vincent 88 88 Ho: 1  2 < 2 H1: 1  2 > 2 n1 = 77 n2 = 83 X1= 16 X2= 13 1 = 5 2 = 7  = 0.05(11) To determine the effect of full-page advertisements in the local newspaper, the owner of an electronic-equipment store asked 200 randomly selected people who visited the store whether they had seen the ad. He also determined whether the customers had bought anything, and, if so, how much they spent. There were 113 respondents who saw the ad. Of these, 49 made a purchase. Of the 87 respondents who did not see the ad, 21 made a purchase. What alternative hypothesis should the owner use if he wishes to determine at the 5% significance level if the ads are worthwhile, i.e., among those who make a purchase, do customers who see the ad spend more on average than those who do not see the ad? A) μ1 – μ2 < 0 B) μ1 – μ2 > 0 C) 021 XX D) 021 XX E) µD > 0 (12) A study classified 394 quick-service restaurants into high-performing and low-performing groups based on their total sales. Each restaurant was rated on a collection of perceived measures of quality by a large number of diners using a 1 to 7 scale. One of the perceived measures was “ordered food served accurately.” The high-sales group had a sample mean score of 5.22 with a standard deviation of 5.11. The low-sales group had a sample mean score of 3.85 with a standard deviation of 1.28. To estimate the difference in mean perception of quality, which of the following formulas is most appropriate? A) DDnDnStXD1;2 B)  222121;221nSnStXX  C)  222121221nnZXX D)  22122;22121nsnstXXppnn (13) Two machines are designed to fill cans with 1 pound of ground coffee.


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OSU BUSMGT 2320 - Comparisons of Two Populations (mu) Additional Practice

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