Cloud seeding has been studied for many decades as a weather modification procedure (for an interesting study of this subject, see the article in technometrics, “a bayesian analysis of a multiplicative treatment effect in weather modification,” 1975, vol. 17, pp. 161–166). the rainfall in acre-feet from 20 clouds that were selected at random and seeded with silver nitrate follows: 18.0, 30.7, 19.8, 27, 1, 22.3, 18.8 31.8, 23.4, 21.2, 27.9, 31.9, 27.1, 25.0, 24.7, 26.9, 21.8, 29.2, 34.8, 26.7, and 31.6. (a) can you support a claim that mean rainfall from seeded clouds exceeds 25 acre-feet? use alpha = 0.01 find the p-value. (b) check that rainfall is normally distributed. (c) compute the power of the test if the true mean rainfall it 27 acre-feet (d) what sample size would be required to detect a true mean rainfall of 27 5 acre-feet if we wanted the power of the test to be at least 0.9? (e) explain how the question in part (a) could be answered by constructing a one-sided confidence bound on the mean diameter.