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The measure of brightness of paper produced by two different processes is recorded below for sam- ples of size 9 drawn randomly from each of two processes. 5 6 7 8 9 Observation Process A 1 2 3 4 6.1 9.2 8.7 8.9 7.6 7.1 9.5 8.3 9.0 Process B 9.1 8.2 8.6 6.9 7.5 7.9 8.3 7.8 8.9 Rank of Process A 1 17 12 13.5 5 3 18 9.5 15 Rank of Process B 16 8 11 2 4 7 9.5 6 13.5 For the original data set Y₁ = 8.2667, YB = 8.1333, SA = 1.11915 and SB = 0.69462. For the rank of the original data set, the rank sum of the process A is 94 and that for the process B is 77. Do the data provide sufficient evidence to suggest a significant difference in location of the bright- ness measurements of the two processes? (a) For a suitable nonparametric procedure formulate appropriate null and alternative hypothe- ses to test the difference in the location of the distributions of the brightness measurements of the two processes. (b) Use the Mann-Whitney U Test, to test the hypotheses in part (a) and comment on the outcome of the test on the basis of the P-value. (e) For a suitable parametric procedure formulate appropriate null and alternative hypotheses to test the difference in the location of the distributions of the brightness measurements of the two processes.

The measure of brightness of paper produced by two different processes is recorded below for sam- ples of size 9 drawn randomly from each of two processes. 5 6 7 8 9 Observation Process A 1 2 3 4 6.1 9.2 8.7 8.9 7.6 7.1 9.5 8.3 9.0 Process B 9.1 8.2 8.6 6.9 7.5 7.9 8.3 7.8 8.9 Rank of Process A 1 17 12 13.5 5 3 18 9.5 15 Rank of Process B 16 8 11 2 4 7 9.5 6 13.5 For the original data set Y₁ = 8.2667, YB = 8.1333, SA = 1.11915 and SB = 0.69462. For the rank of the original data set, the rank sum of the process A is 94 and that for the process B is 77. Do the data provide sufficient evidence to suggest a significant difference in location of the bright- ness measurements of the two processes? (a) For a suitable nonparametric procedure formulate appropriate null and alternative hypothe- ses to test the difference in the location of the distributions of the brightness measurements of the two processes. (b) Use the Mann-Whitney U Test, to test the hypotheses in part (a) and comment on the outcome of the test on the basis of the P-value. (e) For a suitable parametric procedure formulate appropriate null and alternative hypotheses to test the difference in the location of the distributions of the brightness measurements of the two processes.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The measure of brightness of paper produced by two different processes is recorded below for sam- ples of size 9 drawn randomly from each of two processes. Observation Process A Process B Rank of Process A Rank of Process B 1 2 3 4 6.1 9.2 8.7 8.9 9.1 8.2 8.6 6.9 7.5 7.9 8.3 7.8 8.9 17 12 13.5 5 3 18 9.5 15 7 9.5 6 13.5 1 16 8 11 2 4 5 6 7 8 9 7.6 7.1 9.5 8.3 9.0 For the original data set YA = 8.2667, YB = 8.1333, SA = 1.11915 and sp = 0.69462. For the rank of the original data set, the rank sum of the process A is 94 and that for the process B is 77. Do the data provide sufficient evidence to suggest a significant difference in location of the bright- ness measurements of the two processes? (a) For a suitable nonparametric procedure formulate appropriate null and alternative hypothe- ses to test the difference in the location of the distributions of the brightness measurements of the two processes. (b) Use the Mann-Whitney U Test, to test the hypotheses in part (a) and comment on the outcome of the test on the basis of the P-value. (c) For a suitable parametric procedure formulate appropriate null and alternative hypotheses to test the difference in the location of the distributions of the brightness measurements of the two processes.
Transcribed Image Text:The measure of brightness of paper produced by two different processes is recorded below for sam- ples of size 9 drawn randomly from each of two processes. Observation Process A Process B Rank of Process A Rank of Process B 1 2 3 4 6.1 9.2 8.7 8.9 9.1 8.2 8.6 6.9 7.5 7.9 8.3 7.8 8.9 17 12 13.5 5 3 18 9.5 15 7 9.5 6 13.5 1 16 8 11 2 4 5 6 7 8 9 7.6 7.1 9.5 8.3 9.0 For the original data set YA = 8.2667, YB = 8.1333, SA = 1.11915 and sp = 0.69462. For the rank of the original data set, the rank sum of the process A is 94 and that for the process B is 77. Do the data provide sufficient evidence to suggest a significant difference in location of the bright- ness measurements of the two processes? (a) For a suitable nonparametric procedure formulate appropriate null and alternative hypothe- ses to test the difference in the location of the distributions of the brightness measurements of the two processes. (b) Use the Mann-Whitney U Test, to test the hypotheses in part (a) and comment on the outcome of the test on the basis of the P-value. (c) For a suitable parametric procedure formulate appropriate null and alternative hypotheses to test the difference in the location of the distributions of the brightness measurements of the two processes.
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