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Section 10.4.2
Power
AP Statistics
March 11, 2008
CASA
What is Power?
Power is a test of sensitivity.
 Your statistical test may be able to detect
differences, but how well does it detect
difference of a pre-determined nature?
 The Power procedure allows to state the
probability of our procedure to catch the
differences.

AP Statistics, Section 8.2.1
2
Power Procedure




Begin by stating your H0 and Ha as usual.
Find the z* or t* that would allow you to reject
H0.
Find the x-bar that matches up with the z* or t*.
Assuming that you have a particular true mean,
what is the probability that you would be to still
reject the H0?
AP Statistics, Section 8.2.1
3
Power Example: Example 10.23

Can a 6-hour study program increase your
score on SAT? A team of researchers is
planning as study to examine this
question. Based on the result of a previous
study, they are willing to assume that the
change has σ=50. Research would like
significance at the .05 level.
AP Statistics, Section 8.2.1
4
Power Example: Example 10.23

A change of 50 points would be
considered important, and the
researchers would like to have a
reasonable chance of detecting a change
is this large or larger. Is 25 subjects a
large enough sample for this project?
AP Statistics, Section 8.2.1
5
Step 1: State your hypothesis
H0: µ=0
 Ha: µ>0
 Where µ represents the change is in the
SAT score.

AP Statistics, Section 8.2.1
6
Step 2: Find the z* value and find
the data value
x 
 We'll set α=.05,
z* 
invNorm(.95) gives us a
/ n
z*=1.645.
 What is the lowest x-bar
x

0
would show significance?
1.645 
 Summary: If we had a
50 / 25
study with n=25 and xbar>16.45, we would
have significance.


1.645 50 / 25  x
16.45  x
AP Statistics, Section 8.2.1
7
Step 3: Chance at importance
We stated that gains of 50 points would be
considered "important". We state this as
the alternative µ=50.
 The power against the alternative µ=50
increase is the probability that H0 is
rejected when µ=50.
 Restated: What the area from 16.45 to ∞
under a normal curve centered at µ=50.

AP Statistics, Section 8.2.1
8
Step 3
normalcdf(16.45,1E99,50,50/√(25))=.9996
 Summary: because the power is so high,
there is a great chance of finding a
significance when the real increase is 50.

AP Statistics, Section 8.2.1
9
Increase Power by…
increase alpha
 increase sample size

AP Statistics, Section 8.2.1
10
Exercises

10.71-10.77 odd, 10.79-10.89
AP Statistics, Section 8.2.1
11
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