Often data do not satisfy the conditions for use of any of the standard hypothesis-testing procedures that we have discussed-the pooled t-test, non-pooled t-test, or Mann- Whitney test. However, by making a suitable transformation, you can often obtain data that do satisfy the assumptions of one or more of these standard tests.
In the paper "A Bayesian Analysis of a Multiplicative Treatment Effect in Weather Modification" (Technometrics, Vol. 17, pp. 161-166), J. Simpson et al. presented the results of a study on cloud seeding with silver nitrate. The rainfall amounts, in acre-feet, for unseeded and seeded clouds are provided on the Weiss-Stats site. Suppose that you-want to perform a hypothesis test to decide whether cloud seeding with silver nitrate increases rainfall.
a. Obtain box-plots and normal probability plots for both samples.
b. Is use of the pooled t-test appropriate? Why or why not?
c. Is use of the non-pooled t-test appropriate? Why or why not?
d. Is use of the Mann-Whitney test appropriate? Why or why not?
e. Nowtrans-form each sample by taking logarithms. That is, for each observation, x, obtain log x.
f. Obtain box-plots and normal probability plots for both transformed samples.
g. Is use of the pooled t-test on the transformed data appropriate? Why or why not?
h. Is use of the non-pooled t-test on the transformed data appropriate? Why or why not?
i. Is use of the Mann-Whitney test on the transformed data appropriate? Why or why not?
j. Which of the three procedures would you use to conduct the hypothesis test for the transformed data? Explain your answer.
k. Use the test you designated in part (j) to conduct the hypothesis test for the transformed data.
l. What conclusions can you draw?