1. Section 10.4.2 Power AP Statistics March 11, 2008 CASA

2. AP Statistics, Section 8.2.12 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.

3. AP Statistics, Section 8.2.13 Power Procedure Begin by stating your H 0 and H a as usual. Find the z* or t* that would allow you to reject H 0. 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 H 0 ?

4. AP Statistics, Section 8.2.14 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.

5. AP Statistics, Section 8.2.15 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?

6. AP Statistics, Section 8.2.16 Step 1: State your hypothesis H0: µ=0 Ha: µ>0 Where µ represents the change is in the SAT score.

7. AP Statistics, Section 8.2.17 Step 2: Find the z* value and find the data value We'll set α=.05, invNorm(.95) gives us a z*=1.645. What is the lowest x-bar would show significance? Summary: If we had a study with n=25 and x- bar>16.45, we would have significance.

8. AP Statistics, Section 8.2.18 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.

9. AP Statistics, Section 8.2.19 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.

10. AP Statistics, Section 8.2.110 Increase Power by… increase alpha increase sample size

11. AP Statistics, Section 8.2.111 Exercises 10.71-10.77 odd, 10.79-10.89