problemkey_chp14_2 - 8 1. Let F x ( ) be the distribution...

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Solution for Practice Problems: Problem 14.3 1. Let F x ( ) be the distribution for population A and G y ( ) the distribution for population B. Then the hypotheses should be stated as the following H F x G y H F x G y a 0 : ( ) ( ) : ( ) ( ) = 2. Sample A Sample B Obs. 65 35 47 52 Rank 13 6.5 11 12 Obs. 37 40 33 29 42 33 35 28 34 Rank 8 9 3.5 2 10 3.5 6.5 1 5 Test statistic: T =13+6.5+11+12=42.5 From the data sets, n n 1 2 4 9 = = and , under the significance level α = 0 05 . , the rejection region is T T U = 39 . Since the test statistic from the data sets yields T =42.5>39, we should be able to reject the null hypothesis and conclude that the distribution for population A is shifted to the right of that for population B.
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Problem 14.4 Population 1 Population 2 Obs. Rank Obs. Rank 9.0 2 15.6 12 25.6 23 31.1 27 21.1 19 26.9 25 24.6 20 20.0 18 24.7 21 16.5 14 26.0 24 25.1 22 17.2 15 30.1 28 18.7 17 26.1 25 10.1 4 11.1 6 13.5 9 12.0 7 18.2 16 10.3 5 9.2 3 7.0 1 14.2 11 15.8 13 13.6 10 13.2
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Unformatted text preview: 8 1. Let F x ( ) be the distribution for population 1 and G y ( ) be that for population 2, the hypotheses can be stated as the following H F x G y H F x G y a : ( ) ( ) : ( ) ( ) = T A =2+12+23+27+19+26+20+18+21+14+24+22+15+28+17+25 =313 Since both sample sizes are greater than 10, we can use normal distribution theory. Test statistic: z T n n n n n n n A =-+ + + + =-+ + × + + = 1 1 2 1 2 1 2 1 2 1 12 313 16 16 12 1 2 16 12 16 12 1 12 37603 ( ) ( ) ( ) ( ) . Rejection region: z z = 0 05 1645 . . Since the test statistic is inside of rejection region, we can reject the null hypothesis and conclude that the distribution for population 2 is shifted to the left of that for population 1 2. p value P Z-= ≈ ( . ) 376...
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This note was uploaded on 08/30/2011 for the course STA 4164 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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problemkey_chp14_2 - 8 1. Let F x ( ) be the distribution...

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