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Measuring the impact of great Teachers An education study in Tennessee in the 1980’s (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 35 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) Results reported in 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.” (Economist Chetty and Saenz 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!)

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Classroom gamesTwo professors at the University of Arizona were interested in whether having students actually play a game would help them analyze theoretical properties of the game. The professors performed an experiment in which students played one of two games before coming to class where both games were discussed. Students were randomly assigned to which of the two games they played, which we’ll call Game 1 and Game 2. On a later exam, students were asked to solve problems involving both games, with Question 1 referring to Game 1 and Question 2 referring to Game 2. When comparing the performance of the two groups on the exam question related to Game 1, they suspected that the mean for students who had played Game 1 (µ1) would be higher than the mean for the other students, µ2, so they considered the hypothesis .
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