B.52 Measuring the Impact of Great Teachers An education study in Tennessee in t
ID: 3313806 • Letter: B
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B.52 Measuring the Impact of Great Teachers 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,Z0 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 adult-hood. 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 eaming 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!)Explanation / Answer
p-value is a measure that indicates whether or not there exists strong evidence to reject a defined null hypothesis about a population based on analysing sample from it.
The p-value is a number between 0 and 1 and interpreted in the following way:
A small p-value (typically 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.
In other words, p-value is an indication of the likeliness of observation due to randomness than due to a null hypothesis that is wrong. A very small number, therefore, allows us to rule out the possibility of randomness and reject the null hypothesis.
In this research, the null & alternate hypothesis can be defined as follows:
Null Hypothesis H0: Mean Performance of students is the same for groups taught by Outstanding & mediocre Kinder garten teachers
Alternate Hypothesis Ha: Mean Performance of students is significantly different for groups taught by Outstanding & mediocre Kinder garten teachers
a) It is clearly mentioned that some classes did far better than others and differences were too big to be explained by randomness. Based on the explanation of p-value above, the p-value is relatively small and allows us to reject the null hypothesis.
b) Children who had excellent early schooling results did little better on tests than similar children who did not.
The 'little' indicates the possibility of the difference in results being caused due to randomness. So, the p-value is relatively high and doesn't allow us to reject the null hypothesis.
c) Students who were in a class room that made significant gains in kindergarten were significantly "more likely to go to college..etc."
The term 'significantly' indicates that the performance of students taught by outstanding kindergarten teachers were remarkably different from those taught by mediocre kindergarten teachers to an extent that it couldn't have been a result of randomness in samples observed. So, the p-value in this case is relatively small which allows us to reject the null hypothesis.
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