15.4 Body mass reduction and smoking Smoking is a known cause of reduced body mass. To validate this, a researcher randomly selects 7 smokers and 7 nonsmokers and records their individual body mass index. The body mass index data in kg/m2 are:
Smokers: 13.1, 15.2, 16.5, 15.0, 16.4, 19.3, 16.0 Nonsmokers: 19.5, 21.5, 23.5, 18.3, 24.5, 19.6, 18.9

a. State the hypotheses for conducting a one-sided (right tailed) Wilcoxon test.

b. Find the ranks for the two groups and their sum and mean of ranks.

c. Software reports a small-sample one-sided P-value of 0.002. Interpret and explain the significance of the P-value. (You can reproduce these results by entering the data in the Permutation Test for Means web app, selecting Wilcoxon rank sum as the test statistic, and selecting the option for generating all possible permutations.)