Encourage students to use them to solve additional confidence interval exercises from their text or from other sources. We'll be more precisely correct presently. We call the sample-based estimate of the standard deviation of the sampling distribution of the mean, its standard error. Estimating a standard error introduces additional variability in our intervals, as we can see with a simulation. We introduce the t-distribution family as an alternative density that works within the Density tool and see that we construct confidence intervals in much the same way as we did before.
Students can slide the df to see the change in the density.
They learn in this way that changes in degrees of freedom change the width of the confidence interval very little above 10 degrees of freedom. Students discover that the width of a confidence interval for small samples is affected far more by the increase in the standard error due to a small n. They construct confidence intervals with the density tool and learn to construct confidence intervals in Data Desk for real data. Student's t-based procedures are natural in statistics packages because packages can compute the standard deviation and sample size. We introduce an interactive t-table that works in much the same way as the interactive Normal table.