1. Inference as Decision
Section 10.4

2. Type I error If we reject Ho (accept Ha) when in fact Ho is true
Type II error
If we accept Ho (reject Ha) when in fact Ha is true

3. Truth about the population
Decision based on sample
H0 True Ha True
Type I error
Correct Decision
Type II error
Reject H0
Accept H0

4. Significance and Type I error
The significance level  of any fixed level test is the probability of a Type I error
That is ,  is the probability that the test will reject the null hypothesis Ho when Ho is in fact true

5. Power
The probability that a fixed level  significance test will reject Ho when a particular alternative value of the parameter is true is called the power of the test against that alternative

6. The power of a test against any alternative is 1 minus the probability of a Type II error for that alternative
Calculations of power are essentially the same as calculations of the probability of Type II error

7. P-values describe what would happen supposing that the null hypothesis is true
Power describes what would happen supposing a particular alternative is true

8. Calculating Power
State Ho, Ha, the particular alternative we want to detect, and the significance level 
Find the values of x bar that will lead us to reject Ho
Calculate the probability of observing these values of x bar when the alternative is true

9. Four Ways to Increase Power
Consider a particular alternative that if farther away from o
Increase the sample size
Decrease 

10. Practice Problems Section 10.4 Chapter Review pg. 605 #10.74-10.77