ABSTRACT
This chapter begins by considering tests for differences in means, where the observations in different categories are not paired. It illustrates how hypothesis testing is done, and the issues that require consideration. The null hypothesis is that some unobserved parameter is equal to zero, while the alternative hypothesis is that it is greater than zero. The one-sided nature of the alternative hypothesis seems sensible, as we can eliminate the lower tail from consideration since negative values are impossible. For the hypothesis test, the null hypothesis is that there is no change in average test scores, interpreted as always being the average change in an unobserved population of students.
