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AP Statisitics
9.3 Exploring Sampling Distributions
Name:__________________________
Per:_________
For this activity, you will need to log on to a computer. Go to the AP Statistics class blog and click on the link to the Rice
University Sampling Distribution applet. (http://onlinestatbook.com/stat_sim/sampling_dist/index.html)
Before you begin the activity, take a few minutes to read the Instructions on the website to understand the functionality
of the buttons and controls. Then click [BEGIN] to start the simulation.
Understand the Graphs:
The top graph represents the population. The second graph shows the data from a sample of size = 5 (this is the default
and we will leave it set to 5 until later in the activity). The third graph shows the distribution of the sample means.
When you collect one sample, you will have one mean. When you collect additional samples, the means from these
samples will be added to the graph to construct the distribution of sample means. The fourth graph is blank (for now).
Be sure that you clearly understand what each of the 3 graphs represents before you go much further!
Part I: Exploring the Sampling Distribution of x for a Normal Population.
You will use the applet to explore the shape of the sampling distribution when the population is Normally distributed.
Confirm that the top graph is set to “Normal.” This should be the setting for all of the activities in Part I. Press “Clear lower 3” to reset the activity.
1.
Identify the parameters of the population in the chart below (they are shown to the left of the top graph).
Mean (μ)
Median
Std. Dev. (σ)
2.
3.
Click the "Animated sample" button. Five scores from a normal distribution will be sampled and plotted in a histogram. The
mean of the sample will be computed and plotted in a second histogram. Repeat this 5 times or until you understand the how
the "Distribution of Means" is created. The red line extends from the mean one standard deviation in each direction. The
colored vertical bars on the X-axis correspond to the statistic of the same color displayed on the left of the graph.
Click the "5 samples" button to sample 5 samples of 5 scores each (so you should now have 10 samples of 5 scores each). The
five additional means will be plotted. Sketch the sampling distribution below. Describe the sampling distribution using SOCS.
Mean (  x )
Median
Std. Dev. (  x )
4.
Click the "1000 samples" until the distribution of means has stabilized. The sampling distribution of the mean is the distribution
that is approached as the number of samples approaches infinity. With 5,000 to 10,000 samples of 5 scores each, you get a
pretty good approximation. Sketch the sampling distribution below. Describe the sampling distribution using SOCS.
Mean (  x )
Median
Std. Dev. (  x )
5.
Click the “Fit Normal” box next to the sampling distribution to compare the sampling distribution to a Normal population. Does
it appear to be Normal?
6.
Compare the mean of the population to the mean of the sampling distribution.
7.
What is the standard deviation of the population measuring? What is the standard deviation of the sample distribution
measuring? What is the standard deviation of the sampling distribution measuring? Why are they different?
8.
The distribution plotted in (4) above is the sampling distribution of the mean of a sample size of 5. Now we will approximate the
sampling distribution of the mean for other sample sizes by changing the value of n. Click on “Clear bottom 3.” Change the
value to N=10 and repeat step 3 above. Sketch the sampling distribution below. Describe the sampling distribution using SOCS.
Mean (  x )
Median
Std. Dev. (  x )
9.
Click on “Clear bottom 3.” Change the value to N=25 and repeat step 4 above. Sketch the sampling distribution below. Describe
the sampling distribution using SOCS. How does the standard deviation of the sampling distribution change as n changes?
Mean (  x )
Median
Std. Dev. (  x )
10. Describe the shape of the sampling distribution of x when the population is Normally distributed.
Part II: Exploring the Sampling Distribution of x for a non-Normal Population.
You will use the applet to explore the shape of the sampling distribution when the population is not Normally distributed. This time, on the top
graph select “Skewed” population.
11. Identify the parameters of the population in the chart below (they are shown to the left of the top graph).
Mean (μ)
Median
Std. Dev. (σ)
12. Click on the bottom 2 graphs so that both display the mean – one for sample size n = 5 and the other for n = 10. Click the
“animated” button a few times to be sure that you see what is happening. Then “Clear lower 3” and take 10,000 SRSs. Sketch
the sampling distribution for each below. Describe the sampling distribution using SOCS.
N=5
Mean (  x )
Median
Std. Dev. (  x )
N = 10
Mean (  x )
Median
Std. Dev. (  x )
13. Click “Clear lower 3.” Now change the sample sizes to n = 20 and n = 25 and take 10,000 more SRSs. Sketch the sampling
distribution below. Describe the sampling distribution using SOCS. What happens to the shape of the sampling distribution as
the sample size increases?
N = 20
Mean (  x )
Median
Std. Dev. (  x )
N = 25
Mean (  x )
Median
Std. Dev. (  x )
14. Click the “Fit Normal” box next to the sampling distribution to compare the sampling distribution to a Normal population. Does
it appear to be Normal?
15. Compare the mean of the population to the mean of the sampling distribution.
16. Clear the page. Now select “Custom” distribution. Click on parts of the top graph to create a graph of a population with a very
strange shape. Repeat steps 12-15 above. Identify the parameters of the population in the chart below (they are shown to the
left of the top graph).
Mean (μ)
Median
Std. Dev. (σ)
17. Click on the bottom 2 graphs so that both display the mean – one for sample size n = 5 and the other for n = 10. Click the
“animated” button a few times to be sure that you see what is happening. Then “Clear lower 3” and take 10,000 SRSs. Sketch
the sampling distribution for each below. Describe the sampling distribution using SOCS.
N=5
Mean (  x )
Median
Std. Dev. (  x )
N = 10
Mean (  x )
Median
Std. Dev. (  x )
18. Click “Clear lower 3.” Now change the sample sizes to n = 20 and n = 25 and take 10,000 more SRSs. Sketch the sampling
distribution below. Describe the sampling distribution using SOCS. What happens to the shape of the sampling distribution as
the sample size increases?
N = 20
Mean (  x )
Median
Std. Dev. (  x )
N = 25
Mean (  x )
Median
Std. Dev. (  x )
19. What do you conclude about the shape of the sampling distribution of x ?