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Type I error
Ho incorrectly rejected.
Type I error is same as
Significance level of test. Usually small.
Type II error
Ho is incorrectly accepted. Actual value of parameter p is required.
Type II error same as
Acceptance region for true parameter. Usually larger.
Type I error for continuous distribution
Equal to significance level
Size of a test
Probability of rejecting Ho, when true. Same as Type I error.
Power of a test
Probability of rejecting Ho when false. Equal to 1-P(Type II)
Power when correct decisions are being made more often than not
Power > 0.5
What increases power?
Increasing sample size and significance level
Power function of a test
Function of parameter p, which gives probability that test statistic fill fall in critical region of test, if p is true value of parameter.
Which power is better
Test with a higher power is better.
Note 
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