## P-value Exploration

First, use the sliders to select the following:
(1) the sample size, "size", (2) the population mean μ,
(3) the population standard deviation σ , (4) the sample
mean, "xbar", and (5) whether you want a Left Tailed,
Right Tailed, or Two Tailed test.

Next, move the seed slider to generate 20 random
samples of the given size from a normal distribution
with mean μ and standard deviation σ .

Click on the "Use the random samples ..." check box to
find out how many and what proportion of sample means
are as extreme as the selected sample mean, "xbar".

Click on the "Compute the actual P-value" check box to
compute the actual P-value. You should compare the
actual P-value with the empirical P-value computed under
the other checkbox.

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The P-value is the probability that the sample statistic could
be as extreme as it is given that the null hypothesis is true.

This applet generates 20 random samples from a normal
distribution with the given mean μ and the given standard
deviation σ to provide an empirical estimate of how likely
it is to generate a sample mean as extreme as the given
value. The resulting sample proportion is an empirical
estimate of the P-value for this situation.

The actual P-value is computed using the normal distribution.

David Gurney, Created with GeoGebra