## t-Curves compared to the Standard Normal Curve

Statistics,  Prof G. Battaly, Westchester Community College           Class Notes: CI, σ not known

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.

3.  Optional:  Click at the bottom of the slider where df=1.  Then right click on the slider and select "Animation On."
The t-Curve will automatically graph from df=1 to df=30.

[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 it at df=30.]

Optional:  Right click on the slider.  Select Object properties.  On the slider tab, change the max value to 50.  Then click CLOSE at the lower right.
You will see that the slider can now to move to df=50.  At this value, the t-Curve is still not exactly equal to the SNC, but is a bit closer than at df=30.

Prof G. Battaly, Westchester Community College, Statistics

G. Battaly, WCC, Created with GeoGebra