ssrs 2012 barcode font Nonparametric Tests in Software

Printing Quick Response Code in Software Nonparametric Tests

CHAPTER 10 Nonparametric Tests
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and since the sixth, seventh, eighth, and ninth places represent the same height (68 inches), we assign the mean rank 1(6 7 8 9) 7.5 to these places. Thus the sons heights are assigned the ranks 4 1.5 1.5 3.5 3.5 5 7.5 7.5 7.5 7.5 10 11 12 (21)
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Using the correspondences (18) and (19), and (20) and (21), we can replace Table 10-28 with Table 10-29. Table 10-30 shows the difference in ranks, D, and the computations of D2 and gD2, whereby rs 1 6 a D2 N(N 2 1) 1 6(72.50) 12(122 1) 0.7465
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The result agrees well with the correlation coefficient obtained by other methods (see Problems 8.26, 8.28, 8.30, and 8.32). Table 10-29 Rank of father Rank of son 4 7.5 2 3.5 6.5 7.5 3 1.5 8.5 10 1 3.5 11 7.5 5 1.5 8.5 12 6.5 5 10 7.5 12 11
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Table 10-30 D 3.5 1.5 2.25 1.0 1.00 1.5 2.25 1.5 2.25 2.5 6.25 3.5 3.5 3.5 1.5 2.5 1.0 gD2 72.50
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D2 12.25
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12.25 12.25 12.25 2.25 6.25 1.00
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The sign test
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10.26. A company claims that if its product is added to an automobile s gasoline tank, the mileage per gallon will improve. To test the claim, 15 different automobiles are chosen and the mileage per gallon with and without the additive is measured; the results are shown in Table 10-31. Assuming that the driving conditions are the same, determine whether there is a difference due to the additive at significance levels of (a) 0.05, (b) 0.01.
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Table 10-31
With additive 34.7 28.3 19.6 25.1 15.7 24.5 28.7 23.5 27.7 32.1 29.6 22.4 25.7 28.1 24.3
Without additive 31.4 27.2 20.4 24.6 14.9 22.3 26.8 24.1 26.2 31.4 28.8 23.1 24.0 27.3 22.9
10.27. Can one conclude at the 0.05 significance level that the mileage per gallon achieved in Problem 10.26 is better with the additive than without it 10.28. A weight-loss club advertises that a special program that it has designed will produce a weight loss of at least 6% in 1 month if followed precisely. To test the club s claim, 36 adults undertake the program. Of these, 25 realize the desired loss, 6 gain weight, and the rest remain essentially unchanged. Determine at the 0.05 significance level whether the program is effective. 10.29. A training manager claims that by giving a special course to company sales personnel, the company s annual sales will increase. To test this claim, the course is given to 24 people. Of these 24, the sales of 16 increase, those of 6 decrease, and those of 2 remain unchanged. Test at the 0.05 significance level the hypothesis that the course increased the company s sales.
CHAPTER 10 Nonparametric Tests
10.30. The MW Soda Company sets up taste tests in 27 locations around the country in order to determine the public s relative preference for two brands of cola, A and B. In eight locations brand A is preferred over brand B, in 17 locations brand B is preferred over brand A, and in the remaining locations there is indifference. Can one conclude at the 0.05 significance level that brand B is preferred over brand A 10.31. The breaking strengths of a random sample of 25 ropes made by a manufacturer are given in Table 10-32. On the basis of this sample, test at the 0.05 significance level the manufacturer s claim that the breaking strength of a rope is (a) 25, (b) 30, (c) 35, (d) 40.
Table 10-32
41 37 25 43 42 28 32 36 27 33 35 24 22 34 28 38 46 41 27 31 23 30 37 36 24
10.32. Show how to obtain 95% confidence limits for the data in Problem 10.4. 10.33. Make up and solve a problem involving the sign test.
The Mann Whitney U test
10.34. Instructors A and B both teach a first course in chemistry at XYZ University. On a common final examination, their students received the grades shown in Table 10-33. Test at the 0.05 significance level the hypothesis that there is no difference between the two instructors grades.
Table 10-33
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