The applet below allows us to simulate
drawing random samples of VAST test takers from a normally distributed
null population with a mean (m) of 500
and a standard deviation (s)
of 100.

1. To begin, use the drop down menu under Sample size: and select
N=25. Under Show:, check Show sample data and
Show population (with
no other boxes checked for now).

2. Click Draw a sample to draw a random sample of 25 cases
from this population. The individual scores are represented by black
boxes and the sample mean is shown with a red arrow.

3. Click Draw a sample at least ten times to observe how a
sample mean based on N = 25 is likely to be quite close to the
population mean of 500.

4. Click Show obtained means to see your observed sample means.

5. To view the theoretical distribution of all possible sample means
based on samples of N = 25 selected randomly from the Null
Population, click Show
sampling distribution of the mean. The standard deviation
of this distribution is the standard error of the mean, shown in the box
to be equal to 20.00, the value we computed earlier. Click here
to review the computation.

6. To observe the sampling distribution of means for smaller samples
with N = 5, use the drop down menu under Sample size: and
select N=5. Notice that the distribution of possible means has
greater variability. The standard error of the mean is reported in the
box to be 44.72. Review computation.

Question C: Sampling Error

From least to most likely, rank the following events (assume
random sampling from the population of VAST-test takers with
m = 500 and s = 100):

Obtaining an individual score of 550 or greater.

Obtaining a sample mean of 550 or greater with a sample size of 25.

Obtaining a sample mean of 550 or greater with a sample size of 5.