The variation of the unknown estimation errors is exactly the same as the variation of the sample means. The standard error of the mean (sem) is the standard deviation of the distribution of the sampling errors -- the discrepancies between the statistic and the parameter.
In a normal distribution 95% of the observations fall within +/- 1.96 standard deviations from the mean. The following relationship holds:
Java applets are script that is downloaded to your machine. Using a browser that recognizes these applets (such as Netscape 3.0) try Globally Accessible Statistical Procedures
As alpha decreases, what happens to the width of the confidence interval -- in general? WIth an alpha of 0.05, how many samples fall outside of the confidence interval for 1000 total samples? What does theory say about this? With an alpha of 0.025, how many samples fall outside of the confidence interval for 1000 total samples? What does theory say about this?
Central Limit Applet will let you perform the analysis of rolling two die and keeping track of the sum of the spots showing.