*7. Suppose you wanted to see whether a training program helped raise students’

scores on a standardized test. You administer the test to a random sample of students, give them the training program, then readminister the test. For each student, you record the increase (or decrease) in the test score from one time to the next.

*a. What would the null and alternative hypotheses be for this situation?

*b. Suppose the mean change for the sample was 10 points and the accompanying standard error was 4 points. What would be the standardized score that corresponded to the sample mean of 10 points?

*c. Based on the information in part

b, what would you conclude about this situation?

d. What explanation might be given for the increased scores, other than the fact that the training program had an impact?

e. What would have been a better way to design the study in order to rule out the explanation you gave in part d?