Laureysens, et al. (2004) studied the concentration of aluminum in wood from a number of clones of poplar growing in an area with heavy pollution. The same clone was sampled and tested once in August and again in November. The researchers believed that the concentration of aluminum would be shown to be increasing over time and hence higher in November than in August. The following table gives the aluminum concentrations for twelve of the clones. Clone 1 2 3 4 5 6 7 8 9 10 11 12 Aug. 8.1 10.0 16.5 13.6 9.5 8.3 18.3 13.3 7.9 8.1 8.9 13.4 Nov. 11.2 16.3 15.3 15.6 10.5 15.5 12.7 11.1 19.9 20.4 14.2 36.8 Diff. 3.1 6.3 1.2 2.0 1.0 7.2 5.6 2.2 12.0 12.3 5.3 23.4 The data are to be analyzed using the Wilcoxon signed rank test. H0: Values of aluminum concentrations in the 2 months have the same distribution. Ha: Values of aluminum concentrations are systematically larger in November than in August. Fix α = 0.05 What is the observed value of the statistic W+ used for the test of hypotheses? Under the null hypothesis, what are the values of the mean and standard deviation, respectively, of the statistic W+? Using the Normal approximation, what is the standardized value z of W+ used in testing the null hypothesis?
Laureysens, et al. (2004) studied the concentration of aluminum in wood from a number of clones of poplar growing in an area with heavy pollution. The same clone was sampled and tested once in August and again in November. The researchers believed that the concentration of aluminum would be shown to be increasing over time and hence higher in November than in August. The following table gives the aluminum concentrations for twelve of the clones.
Clone 1 2 3 4 5 6 7 8 9 10 11 12
Aug. 8.1 10.0 16.5 13.6 9.5 8.3 18.3 13.3 7.9 8.1 8.9 13.4
Nov. 11.2 16.3 15.3 15.6 10.5 15.5 12.7 11.1 19.9 20.4 14.2 36.8
Diff. 3.1 6.3 1.2 2.0 1.0 7.2 5.6 2.2 12.0 12.3 5.3 23.4
The data are to be analyzed using the Wilcoxon signed rank test.
H0: Values of aluminum concentrations in the 2 months have the same distribution.
Ha: Values of aluminum concentrations are systematically larger in November than in August.
Fix α = 0.05
What is the observed value of the statistic W+ used for the test of hypotheses? Under the null hypothesis, what are the values of the mean and standard deviation, respectively, of the statistic W+?
Using the Normal approximation, what is the standardized value z of W+ used in testing the null hypothesis?
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
