An education study in Tennessee in the 1980s (known as Project Star) randomly assigned 12,000 students to kindergarten classes, with the result that all classes had fairly similar socioeconomic mixes of students. The students are now about 30 years old, and the study is ongoing. In each case below, assume that we are conducting a test to compare performance of students taught by outstanding kindergarten teachers with performance of students taught by mediocre kindergarten teachers. What does the quoted information tell us about whether the p-value is relatively large or relatively small in a test for the indicated effect?

(a) On the tests at the end of the kindergarten school year, ‘‘some classes did far better than others. The differences were too big to be explained by randomness.”

(b) By junior high and high school, the effect appears to be gone: ‘‘Children who had excellent early schooling do little better on tests than similar children who did not.”

(c) The newest results, reported in July 2010 by economist Chetty, show that the effects seem to re-emerge in adulthood. The students who were in a classroom that made significant gains in kindergarten were significantly ‘‘more likely to go to college, . . . less likely to become single parents, . . . more likely to be saving for retirement, . . . Perhaps most striking, they were earning more.” (Economists Chetty and Saez estimate that a standout kindergarten teacher is worth about $320,000 a year in increased future earnings of one class of students. If you had an outstanding grade-school teacher, consider sending a thank you note!)