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) Showing all work, use the 5 steps of Hypothesis testing,
(b) Sketch the distributions involved,
(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.