Assignment:
Consider the following population of 7 scores:
|
Subject
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
|
Score
|
6
|
3
|
9
|
4
|
6
|
8
|
2
|
(This is a toy example created to help you cement the concept of sampling distribution of the mean. Of course the population mean of its 7 scores can be easily computed exactly and without any need for sampling to estimate it, but we will pretend otherwise for the sake of learning. In real situations, sampling is required because it would be too costly/difficult to examine each member of the very large populations we are typically interested in)
a. List all possible different samples of 4 subjects (n= 4) that can be obtained from this population (you should get 35 samples in total) and compute the sample mean for each sample. The distribution of the 35 sample means is the ‘sampling distribution of the mean' with n = 4 based on the ‘parent' population given by the table above.
The format for each sample should be {Subject Numbers} [Scores] (mean):
Hint: {1,2,3,4} [6,3,9,4] (5.5);
b. Compute the population mean of the ‘parent' population (the scores in the table above) and the mean of the sampling distribution of the mean. Compare the two and interpret.
c. Using STATA, graph a histogram of the sampling distribution of the mean. Describe the shape of the distribution. Is it normal or not? Explain why the distribution is normal (or not).Hint: First, you have to create a data set with the means in STATA.