B4090.HW8 - BTRY 4090 STSCI 4090 Spring 2011 Homework 8 Due...

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BTRY 4090 / STSCI 4090 Spring 2011 Homework 8 Due at 2:00pm on Friday, April 8 in 1198 Comstock Hall 1. If the variances of two normal populations are unequal, the result can greatly affect the true error rate of a test with nominal significance level 0.05 based on the assumption of equal variances. Demonstrate this by performing two computer simulations as follows: (a) Draw a sample of size n 1 = 15 from the normal 2 ( 0, 1/ 25) distribution. Draw a sample of size n 2 = 30 from the normal 2 ( 0, 1) distribution. Compute the t statistic given in Theorem 9.2.2, and determine whether t is in the rejection region of the two-sided test given in the theorem. Do 5,000 simulation runs (or repetitions) of this process, and report the proportion of t values leading to rejection of H 0 . (b) Repeat the simulation of (a), but now draw the first sample of size n 1 = 15 from the normal 2 ( 0, 25) distribution. (c) State your conclusion from (a) and (b). Use your (non-computer) knowledge of normal distributions to make this statement as general as possible. 2. With data consisting of two independent random samples, 2 1 ,..., ~ IID normal( , ) n X X X X and 2 1 ,..., ~ IID normal( , ) m Y Y Y Y
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