Power of a Hypothesis Test

Remember the $\beta$  (Type II Error) ? There is one convenient way to test the performance of a hypothesis test by determining the probability of not making a Type II error. It is called power of the test: $1-\beta$. In fact, it is the probability of rejecting H0 when it is really false.

Here is the illustration of the beta:
>> normspec([-inf,1.645],3,1)
ans =
    0.0877

>> l=linspace(-4,4,100);
>> n=normpdf(l,0,1);
>> hold on;
>> plot(l,n,'r')
>> title("Power = 0.0877")

And here is for the power

>> normspec([1.645,inf],3,1)
ans =
    0.9123

>> plot(l,n,'r')
>> title('Power = 1-Beta = 0.9123')