tCurves 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
tCurve in red.
The slider can be used to change the value for degrees of freedom (df) for the
tCurve. df = n1, where n is the sample size. The tCurve 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
tCurve is for df=1. Describe how this differs from the SNC. __________________.
2. There is a different
tCurve for each df. Click and drag the slider from df=1 to df=30, and watch how the
tCurve changes.
3. Optional: Click at the bottom of the
slider where df=1. Then right click on the slider and select
"Animation On."
The tCurve
will automatically graph from df=1 to df=30.
[1. You should notice that for df=1, the
tCurve 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
tCurve 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 tCurve is still not exactly equal to the SNC, but is a
bit closer than at df=30.
Prof G. Battaly, Westchester Community College, Statistics
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