Twenty students randomly assigned to an experimental group receive an instructional program; 30 in a control group do not. After 6 months, both groups are tested on their knowledge. The experimental group has a mean of 38 on the test (with an estimated population standard deviation of 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the .05 level, what should the experimenter conclude?
(a) Use the steps of hypothesis testing,
(b) sketch the distributions involved, and
(c) explain your answer to someone who is familiar with the t test for a single sample but not with the t test for independent means.