In the 1980s, Tennessee conducted an experiment in which kindergarten students w

Question

In the 1980s, Tennessee conducted an experiment in which kindergarten students were randomly assigned to “regular” and “small” classes, and given standardized tests at the end of the year. (Regular classes contained approximately 24 students, and small classes contained approximately 15 students.) Suppose that, in the population, the standardized tests have a mean score of 925 points and a standard deviation of 75 points. Let SmallClass denote a binary variable equal to 1 if the student is assigned to a small class and equal to 0 otherwise. A regression of TestScore on SmallClass yields

a. Is the estimated effect of class size on test scores statistically significant? Carry out a test at the 5% significance level.

b. Construct a 99% confidence interval for the effect of SmallClass on TestScore.

Explanation / Answer

A) Is the estimated effect of class size on test scores statistically signicant? Carry out a test at the 5% level.

The t-stat is tact = 13.9/2.5= 5:56, which has a p-value of 0.00. Thus the null hypothesis is rejected at the 5% and 1% level.

B) Construct a 99% confidence interval for the effect of SmallClass on TestScore

99% CI: [13.9 (+-)2.58*2.5], [7.45, 20.35]

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