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.
Survey Simulation Exercise
If you would like to try the simulation exercise from today's lecture, you can save survey.do or survey2.do to your hard disk. You can also use these examples as a starting point for your own simulation exercises.