As part of a recent survey, self-reported heights, x, and measuremed heights, y,
ID: 3241922 • Letter: A
Question
As part of a recent survey, self-reported heights, x, and measuremed heights, y, were obtained for males aged 12-16. use the wilcoxon signed-ranks test to test the claim that the matched pairs have differences that come from a population with the median equal to zero at ta significance level of a=0.02
x 61 68 66 60 65 66 63 62 61 67 60 61
y 62.4 62.4 66.4 61.0 63.4 61.2 63.6 61.9 64.6 64.8 67.5
First identify the null alrernative hypothesis.
H0:
*The population of differences has a median equal to at least 1.
*The population of differences has a median not equal to 0.
*The population of differences has a median equal to almost 2.
*The population of differences has a median equal to 0.
H1:
*The population of differences has a median equal to at least 1.
*The population of differences has a median not equal to 0.
*The population of differences has a median equal to almost 2.
*The population of differences has a median equal to 0.
Calculate the test statistic/
T=___
Calculate the critical value.
The critical value is ___
What is the conclusion for this hypothesis test?
A. Fail to reject H0. There is insufficient evidence to warrent rejection of the claim of no difference.
B. Fail to reject H0. There is sufficient evidence to warrent rejection of the claim of no difference.
C. Reject H0. There is insufficient evidence to warrent rejection of the claim of no difference.
D. Reject H0. There is sufficient evidence to warrent rejection of the claim of no difference.
Explanation / Answer
H0: The population of differences has a median equal to 0.
H1: The population of differences has a median not equal to 0.
From the given data,
Test Statistic
T = min(35,43) = 35
Critical value = 9 at n = 12 and 2% los in Signed Rank Test Tables
Here T value > T critical value, So we accept H0
Thus we conclude that the population of differences has a median equal to 0.
Correct Answer: B. Fail to reject H0. There is sufficient evidence to warrent rejection of the claim of no difference.
Di |Di| Rank of Positive Negative X Y Differences Abs Diff Abs Diff Ranks Ranks 61 62.4 -1.4 1.4 3 3 68 62.4 5.6 5.6 10 10 66 66.4 -0.4 0.4 1 1 60 66.4 -6.4 6.4 11 11 65 61 4 4 8 8 66 63.4 2.6 2.6 7 7 63 61.2 1.8 1.8 4 4 62 63.9 -1.9 1.9 5 5 61 61.9 -0.9 0.9 2 2 67 64.6 2.4 2.4 6 6 60 64.8 -4.8 4.8 9 9 61 67.5 -6.5 6.5 12 12 Total; 35 43Related Questions
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