Question

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,” Vol. 17, 1975, 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 an appropriate test to answer the question with α = 0.01, and check

whether the assumptions to use the test is reasonable.

b) Compute the power of the test if the true mean rainfall is 27 acre-feet.

c) 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?

d) Answer the question in part (a) by constructing a one-sided confidence bound

on the mean diameter.