12. The local school district is comparing two methods for teaching mathematics to third-grade children. One class of n = 20 students is being taught by method A and another class of n = 20 is being taught by method B. At the end of the school year, all of the students take a standardized math achievement test. The scores for the students taught by method A produced a mean of M = 75 with 55 = 1800, and the students taught by method B had a mean of M = 87 with 55 = 2000.

a. Compute the pooled variance for the two samples.

b. Take the square root of the pooled variance to obtain a measure of the pooled standard deviation.

Using the pooled standard deviation for both groups, you should be able to describe (or sketch)

the two sample distributions. Based on your description

(or sketch) does there appear to be a difference between the two teaching methods? (That is, are there two separate distributions or do all the scores seem to blend together into a single distribution?)

c. Perform the hypothesis test, using a two-tailed test with a = .05, to determine whether there is a significant difference between the two methods. Do the results of the test agree with your decision from part (b)?