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A researcher wants to estimate the proportion of people who report the side
effect of nausea when taking a drug to reduce anxiety. Of 25 people who take
the drug, 8 report nausea. In this sample, therefore, 0.32 of the patients reported
nausea. Most likely the researcher would construct a confidence
interval on the population proportion. The procedure for constructing a
confidence interval assumes that the sampling distribution of p is normal. Since
the sample proportion, p, can be thought of as the mean of N scores, each score
being either zero or one, the central
limit theorem is applicable. This theorem states that as N increases, the
sampling distribution of the mean (p in this case) approaches a normal distribution.
But how large an N is big enough? The population proportion, Pi, is another
factor that affects the shape of the distribution. The closer Pi is to 0.5,
the more normal the sampling distribution.

This applet allows you to explore the validity of confidence intervals on a
proportion with various values of N and Pi. After you specify N, Pi, the level
of confidence, and the number of simulations you wish to perform, the applet
samples data according to your specification and computes a confidence interval
for each simulation. The proportion of simulations for which the confidence
interval contains Pi is recorded. If the method for constructing confidence
intervals is valid, then about 95% of the 95% confidence intervals should contain
Pi.