Confidence Interval Simulation

Prerequisites
prerequisites

The 95% interval contains the parameter in question (the population mean of 50 in this case) 0.95 of the time. Naturally, the interval does not contain the parameter 0.05 of the time. The 99% interval contains the parameter 0.99 of the time.

The 99% interval is wider than the 95% interval. The larger the sample size, the shorter the interval. Sample size does not affect the proportion of the time the interval contains the parameter.