hw5 - Homework 5(due Mar 17 1 Suppose we would like to...

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Homework 5 (due Mar. 17) 1. Suppose we would like to detect a difference of δ in a test on the mean with a two-sided alternative with probability 0.95 (and α = 0 . 05). We are interested in the required sample size in two cases: when the standard deviation is known to be equal to 3 and it has been estimated to be 3. Find the corresponding sample sizes using Minitab if a) δ = 1; b) δ = 3; c) Compare the relative differences in sample sizes in a) and b). Comment on where it is larger and why. 2. Cloud-seeding has been studied as a weather modification procedure. 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, 31.6. You can use Minitab to solve this problem. a) Can you support a claim that mean rainfall from seeded clouds exceeds 25 acre-feet? Use α = 0 . 01. 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

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