1.One sample has SS = 60 and a second sample has SS = 48.

a.If n = 7for both samples, find each ofthe sample variances and calculatethe

pooled variance. Because the samples are the same size, you should find that the

pooled variance is exactly halfway between the two sample variances.

b.Now assume that n = 7 for the first sample and n = 5for the second. Again,

calculate the two sample variances and the pooled variance. You should find that

the pooled variance is closer to the variance for the larger sample.

2.Two separate samples receive different treatments. After treatment, the first sample has

n = 6withSS = 236, and the second has n = 12 with SS = 340.

a.Computethe pooled variance for the two samples.

b.Calculate the estimated standard error for the sample mean difference.

c.Ifthe sample mean difference is 7points, is this enough to reject the null

hypothesis using a two-tailed test with= .05 level?

3.In a classic study in the area of problem solving, Katona (1940) compared the effectiveness of two methods of instruction. One group of participants was shown the exact, step-by-step procedure for solving a problem and was required to memorize the solution. Participants in a second group were encouraged to study the problem and find the solutionon their own. They were given helpful hints and clues, but the exact solution was never explained. The study included the problem in the following figure showing a pattern of five squares made of matchsticks. The problem is to change the pattern into exactly four squares by moving only three matches. (All matches must be used, none can be removed, and all the squares must be the same size.) After three weeks, both groups returned to be tested again. The two groups did equally well on the matchstick problem they had learned earlier. But when they were given new problems (similar to the matchstick problem), the memorization group had much lower scores than the group who explored and found the solution on their own. The following data demonstrate this result.

Find a SolutionMemorization

On Your Ownof the Solution

n = 8n = 8

M = 10.50M = 6.16

SS = 108SS = 116

a.Isthere a significantdifferencein performance on new problems for these two groups?Use a two-tailed test with =.05.

b.Construct a 90% confidence interval to estimate the size of themean difference.