The rank-sum test is sometimes thought of as a test for population medians. Under the assumptions of equal spread and shape, the means of two populations will differ if and only if the medians differ; therefore tests for equality of population means are also tests for equality of population medians. This exercise illustrates that when these assumptions are seriously violated, the rank-sum test can give misleading results concerning the equality of population medians. Consider the following two samples: X: 2 3 4 5 6 20 40 50 60 70 80 90 100 Y: -10 -9 -8 -7 -6 -5 -4 20 21 22 23 24 25 26 27 Show that both samples have the same median. Compute the P-value for a two-tailed rank-sum test. If small P-values provide evidence against the null hypothesis that the population medians are equal, would you conclude that the population medians are different? Do the assumptions of the rank-sum test appear to be satisfied? Explain why or why a. b. C. not.

The rank-sum test is sometimes thought of as a test for population medians. Under the assumptions of equal spread and shape, the means of two populations will differ if and only if the medians differ; therefore tests for equality of population means are also tests for equality of population medians. This exercise illustrates that when these assumptions are seriously violated, the rank-sum test can give misleading results concerning the equality of population medians. Consider the following two samples: X: 2 3 4 5 6 20 40 50 60 70 80 90 100 Y: -10 -9 -8 -7 -6 -5 -4 20 21 22 23 24 25 26 27 Show that both samples have the same median. Compute the P-value for a two-tailed rank-sum test. If small P-values provide evidence against the null hypothesis that the population medians are equal, would you conclude that the population medians are different? Do the assumptions of the rank-sum test appear to be satisfied? Explain why or why a. b. C. not.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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