STAT 515 - Section 8.6 Supplement
Brian Habing - University of South Carolina
Last Updated: November 1, 2002
Once the power has been calculated (like in the example on pages 359-361), it is
necessary to have a way of easily displaying those results. One of the most common
ways of doing this is to simply plot the power at each of the possible values of the
parameter. So, for the example we would need to plot the points:
a) µ=2,400 power= 0.05
b) µ=2,425 power = 1 - 0.7764 = 0.2236
c) µ=2,450 power = 1 - 0.4522 = 0.5478
d) µ=2,475 power = 1 - 0.1562 = 0.8438
Looking at the above curve then we can see what the probability of correctly rejecting the
null hypothesis for each of the possible true values of the mean. For example the test has
a nearly 100% chance of performing correctly if the actual mean is greater than 2525. On
the other hand it is less than 20% chance of it performing correctly if the actual mean is
less than 2410.
Why is it that the curve will always pass through the point corresponding to the null
hypothesis value and the α-level? Why will it always go to zero or one at the extremes?
