# OSU BUSMGT 2320 - Comparisons of Two Populations (mu) Additional Practice (4 pages)

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## Comparisons of Two Populations (mu) Additional Practice

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- Pages:
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- School:
- Ohio State University
- Course:
- Busmgt 2320 - Decision Sciences: Statistical Techniques

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Comparisons 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 Ho 1 2 1 7 n1 20 X 1 25 2 s1 4 0 05 H1 1 2 1 7 n2 35 X 2 20 4 s2 7 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 1 2 Express your answer to 3 decimal places d Reject Do not reject null hypotheses e Conclusion 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 1 2 3 4 5 6 7 8 9 10 Appraiser 1 1650 360 640 1010 890 750 440 1210 520 690 Appraiser 2 1400 380 600 920 930 650 410 1080 480 770 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 x D 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 Ho 1 2 2 n1 77 X 1 16 1 5 H1 1 2 2 n2 83 X 2 13 2 7 0 05 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 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 1 2 0 B 1 2 0 C X 1 X 2 0 D X 1 X 2 0 E D 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 X D t SD 2 nD 1 nD B X1 C X1 X2 Z D X1 X2 t X2 t 2 S12 n1 2 2 S 22 n2 2 1 2 2 n1 n2 n1 n2 2 s 2p s 2p n1 n2 13 Two machines are designed to fill cans with 1 pound of ground coffee Assume the standard deviations of fill weights for the machines are known to be 0 20 oz for machine 1 and 0 25 oz for machine 2 Independent random samples of cans are selected from the two machines Twenty five cans were selected from machine 1 and yielded an average weight of 15 96 oz Twenty cans were selected from machine 2 and yielded …

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