The applets in this section allow you to see how levels of confidence are achieved through repeated sampling.
The confidence intervals are on p, the probability of a success in a binomial experiment (e.g. coin flip).
In a binomial experiment we are interested in estimating = P(success).
Our estimate for is
 (1) 
For sufficiently large n, and min[n,n(1)]>5 then (1) has an asymptotically normal distribution given by
 (2) 
Using the distribution in (2) we can construct a (1)100% confidence interval by
 (3) 
The three parameters that effect the width of the confidence interval in (3) are:
 n, the sample size,
 the size of , and
 the size of , the level of confidence.
As noted above, the reliability of the confidence interval is dependent upon the size of n and .
The following applets allow you to change each parameter either separately or simultaneously.
For each applet, x will denote the number of successes out of n independent Bernoulli trials.
Each time the Compute! button is pressed, 25 new samples are created for specified n, , and confidence level.
You should expect to see approximately (1)100% of the intervals capturing the true value of .
See also: Central Limit Theorem, Normal Distribution.
