A simple comparative experiment uses a balanced design and randomizes 2r experim

Question

A simple comparative experiment uses a balanced design and randomizes 2r experimental units to two treatments (1 and 2). A response y is measured, and the following output from SAS is used to conduct a test of equality of means (H_0: mu_1 = mu_2) against a two-sided alternative. What is n? (Note that n is used differently in our textbook.) What is the estimated difference due to treatment? What is the standard error of the estimate in part (b)? Report the sample variance for the 10 observations from treatment 1. Repeat for treatment 2. Report the ratio of the sample variances from the two treatments. Give the ratio of expected values of the sample variances from the two treatments, under the assumption of homogeneity of variance.

Explanation / Answer

Answer:

a). n1=10, n2=10 and

n=n1+n2=10+10

=20

b). mean difference = 3.982-6.332= -2.35

c). standard error = 1.1662

d).

sample variance of treatment 1 = 2.64582 = 7.00025764

sample variance of treatment 2 = 2.5692 = 6.599761

e) Variance ratio = 1.06

f). Under assumption of homogeneity of variances, ratio of expected value of sample variances = 1

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