November 02, 2004
Confidence Intervals
We start with the normal approximation to the distribution of a sample proportion with a sample size of n.
Following one of the homework problems, the standard deviation of the sample proportion is 0.0158 for n = 250. We calculated a probability.
The core of the confidence interval concept is the following algebra.
We frequently apply the lemma that p(1-p) = 0.25, more or less.
The true is fixed, but unknown. The confidence interval, which is centered on the sample proportion, moves around (is stochastic). There is a 95% probability that a 95% confidence interval includes the true parameter value.
We considered samples of size 100, 1,000, 10,000, and 1,000,000. At $1 per observation, collecting a sample large enough to accurately estimate p could get expensive.
