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Section 10.4.2
AP Statistics
March 11, 2008
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
AP Statistics, Section 8.2.1
Power Procedure
Begin by stating your H0 and Ha as usual.
Find the z* or t* that would allow you to reject
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
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
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
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
Step 2: Find the z* value and find
the data value
x 
 We'll set α=.05,
z* 
invNorm(.95) gives us a
/ n
 What is the lowest x-bar
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
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
Step 3
 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
Increase Power by…
increase alpha
 increase sample size
AP Statistics, Section 8.2.1
10.71-10.77 odd, 10.79-10.89
AP Statistics, Section 8.2.1
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