3. 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, 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 = TestScore = 918.0 + 13.9 × SmallClass, R2 = 0.01, SER = 74.6 (1.6) (2.5) (a) Do small classes improve test scores? By how much? Is the effect large? Explain. (b) Is the estimated effect of class size on test scores statistically significant? Carry out a test at the 5% level. (c) Construct a 99% confidence interval for the effect of SmallClass on TestScore. (d) Does least squares assumption 1 plausibly hold for this regression. Explain.
3. 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, 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 = TestScore = 918.0 + 13.9 × SmallClass, R2 = 0.01, SER = 74.6 (1.6) (2.5)
(a) Do small classes improve test scores? By how much? Is the effect large? Explain.
(b) Is the estimated effect of class size on test scores statistically significant? Carry out a test at the 5% level.
(c) Construct a 99% confidence interval for the effect of SmallClass on TestScore.
(d) Does least squares assumption 1 plausibly hold for this regression. Explain.
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