Chapter 10.4, Problem 1LC

A researcher is using an independent-measures design to evaluate the difference between two treatment conditions with n = 8 in each treatment. The first treatment produces M = 63 with a variance of s² = 18, and the second treatment has M = 58 with s² = 14.

a. Use a one-tailed test with $\alpha$ = .05 to determine whether the scores in the first treatment are significantly greater than the scores in the second. (Note: Because the two samples are the same size, the pooled variance is simply the average of the two sample variances.)

b. Predict how the value for the t statistic would be affected if the two sample variances were increased to s² = 68 and s² = 60. Compute the new t to confirm your answer.

c. Predict how the value for the t statistic for the original samples would be affected if each sample had n = 32 scores (instead of n = 8). Compute the new t to confirm your answer.