March 23, 2004
Confidence Intervals
Confidence intervals augment a point estimate of a parameter with a statement about a reasonable range of uncertainty.
The Central Limit Theorem is the major theory supporting confidence intervals.
We rearrange a true probability statement with the sample mean in the middle of a double inequality into a true probability statement with the expected value in the middle.
You had to be there to really appreciate this artwork, but it's here for everybody to ponder.
Our first application constructs a confidence interval for a sample proportion.
Condsidering sample sizes of 100 and 10,000 illustrates the square root rule governing the length of confidence intervals.
This analysis also makes us aware of how inaccurate a sample proportion is as an estimate of probability when the sample size is as small as 100.