In the 1980s, Tennessee conducted an experiment in which kindergartenstudents were randomly assigned to “regular” and “small” classes and givenstandardized 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 "TestScore" = 918.0 + 13.9 X SmallClass, R2 = 0.01, SER = 74.6. (1.6) (2.5)a. Do small classes improve test scores? By how much? Is the effectlarge? 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 onTest Score.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
In the 1980s, Tennessee conducted an experiment in which kindergartenstudents were randomly assigned to “regular” and “small” classes and givenstandardized 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 "TestScore" = 918.0 + 13.9 X SmallClass, R2 = 0.01, SER = 74.6. (1.6) (2.5)a. Do small classes improve test scores? By how much? Is the effectlarge? 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 onTest Score.
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