t-Curves compared to the Standard Normal Curve

The following diagram shows the Standard Normal Curve (SNC) in green and the t-Curve in red. The slider can be used to change the value for degrees of freedom (df) for the t-Curve. df = n-1, where n is the sample size. The t-Curve is used for inferences when the population is normally distributed or the sample size, n, is large, and the population standard deviation is NOT known. 1. The opening t-Curve is for df=1. Describe how this differs from the SNC. __________________. 2. There is a different t-Curve for each df. Click and drag the slider from df=1 to df=30, and watch how the t-Curve changes.
[1. You should notice that for df=1, the t-Curve is wider at the base and shorter at the center than the SNC.] [2. As you move the slider from df=1 to df=30, the t-Curve approaches the SNC, coming very close to equivalent at df=30.] Prof G. Battaly, Westchester Community College, Statistics www.battaly.com/stat/