3. Laureysens et al. (2004) measured metal content in the wood of 13 poplar clon
ID: 3156285 • Letter: 3
Question
3. Laureysens et al. (2004) measured metal content in the wood of 13 poplar clones growing in a polluted area, once in August and once in November. Concentrations of aluminum (in micrograms of Al per gram of wood) are shown below
(a) Which parametric inference method corresponds to this problem? What are the null and alternative hypotheses for this test? What are the necessary assumptions for this method?
(b) Which nonparametric test should be used for this test? What are the null and alternative hypotheses for this test? What are the necessary assumptions for this method?
(c) Compute the test statistics W+ and W? (Use November - August for the difference). Show your work.
(d) State the null and alternative hypotheses for testing if the November aluminum levels are higher than the August levels.
Explanation / Answer
(a) A paired saample t-test corresponds to this problem. The hypothesis of testing are:
The necessary assumptions for this method are:
(b) Wilcoxon signed rank test should be used for this test. The hypothesis of testing are:
The necessary assumptions for this method:
(c). We have
Thus, W+ = sum of positive ranks = 65 and W- = sum of abs(negative ranks) = 26
(d) The hypothesis of testing are:
(e) The p-value = 0.021 < 0.05, hence we reject the null hypothesis and conclude that the November aluminum levels are higher than the August levels.
Clone August November Nov - Aug Signed Rank 1 18.3 12.7 -5.6 -6 2 13.3 11.1 -2.2 -9 3 16.5 15.3 -1.2 -11 4 12.6 12.7 0.1 13 5 9.5 10.5 1 12 6 13.6 15.6 2 10 7 8.1 11.2 3.1 8 8 8.9 14.2 5.3 7 9 10 16.3 6.3 5 10 8.3 15.5 7.2 4 11 7.9 19.9 12 3 12 8.1 20.4 12.3 2 13 13.4 36.8 23.4 1Related Questions
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