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| | This applet illustrates the Central Limit Theorem (CLT).
Students can explore and discover the theorem instead of being
told what it says. You can either start the Central Limit Theorem
Illustrator itself, or the HypoCentral applet, a combination of the CLT
Illustrator and simple Hypothesis Testing (which is closely related to the CLT).
If you do not see any buttons above, please
install the Java Runtime Environment (JRE)
plugin, then revisit this page.
 | Start the Central Limit Theorem Illustrator (install the JRE
first if necessary) |
| When the applet is loaded, check the "Slow Motion" checkbox |
| Click on [Start] to select a random sample, compute its mean, and add it
to a bar chart of sample means. |
| Repeat that process until you understand how the blue bar chart is
generated |
| Now uncheck the "Slow Motion" checkbox to speed up the process |
Next answer the following questions:
| Experiment with different distributions (click on [Pick] to choose another
distribution). What shape does the distribution of the sample means (blue
chart) have? Is that true regardless of the underlying population
distribution (yellow chart)? |
| What is the mean for the distribution of the sample means (blue chart) in
relation to the mean of the distribution of the original distribution
(yellow chart)? |
| Is there a relation between the standard deviation of the sample means
(blue chart) and that of the original population (yellow chart)? Experiment
with sample sizes 16, 25, 36, 49, and 64 to find the relation |
If you can answer these questions, you can make up a generalized statement
along the following lines:
If you have a population with an arbitrary distribution with a given
mean mu and standard deviation sigma, and you select random
samples of size N from that population, then the distribution of those
sample means has a ____________ distribution with mean ___________ and
standard deviation ___________.
That theorem is called the Central Limit Theorem.
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