Confidence Interval

The width of the confidence interval increases as the confidence level increases, since with a greater width one is more likely to have included the true mean.

In the previous menu, the Baby Weight Activity uses a confidence interval. The activity assumes that you have access to Excel, a TI-83 calculator or another software package capable of performing descriptive tests. To see the actual math used in finding a confidence interval, go to Confidence Interval Math.

Confidence intervals allow us to make statements about the true value of a population parameter (e.g., mean, Q₁, etc.) based on a random sample. For example, the sample mean (X) of a random population sample is an estimate of, and will not necessarily be equal to, the true mean of the population (µ). The (1-α)100% confidence interval for the population mean (µ) represents a range of values around the sample mean (X) that should include the true (unknown) mean for about (1-α)100% of the samples we may take/observe (e.g., α=0.05 yields a 95% CI(µ)).

The above Java Applet is a visual representation of this notion of confidence. Select the number of samples to be generated from a normal distribution N(µ, σ²), the sample-size for each sample and click PLAY. The short horizontal blue lines are the simulated data points (computer generated). Each vertical red line represents a confidence range for the sample. A green oval underneath some confidence intervals indicates the intervals that do not include the true mean for the population.

Validate that constructing 100 95% CI(µ) generates about %5 (five) intervals that miss the true value being estimated (µ=0). How do the constructed CI's depend on the sample-size and the confidence level (α)? Note that in any given series of experiments random chance error may cause you to get a few more or a few less covering intervals than the target number.

Student Demos (part of SOCR):