Answer Happy

а 1. Let X1, X2, X3, X4 be a random sample from a N(u, 1) distribution, where u is unknown. Suppose that we have observed the following values 2.82, 2.71, 3.22, 2.67 We would like to decide between Ho :μ = 2 Ha:p #2 (a) Find the power of this test for u = 1 and a = 0.01, 05 and 0.1 respectively. (b) How does the power change with respect to a? (c) Review the last problem of the previous homework and answer how the power changes with respect to sample size n.

1 2. Let X1, X2, ..., X100 be a random sample from an unknown distribution. After observing this sample, the sample mean and the sample variance are calculated to be I = 21.32, $2 = 27.6 Design a level 0.05 test to choose between Ho : A = 20 = Ha:u > 20 : (a) Do you accept or reject H ? (b) What is the power of this test for u = 22?

4. A movie theater wants to know if there is relationship between movie types and snacks. The following data are collected from 600 randomly selected guests. Movie Type Action Comedy Family Horror Row Totals Snacks 50 125 90 45 310 No Snacks 75 175 10 290 Column Totals 125 120 Grand Total = 600 Test the hypothesis with a significance level of 0.05. 30 300 55