The power function is the probability of rejecting the null hypothesis.
hence
Now X is a binomial rv with n=20 and p anything you wish in [0,1]
So
OR
We just learned this today so I am just slightly confused on how this stuff works. Any hints or starters would be great!! Thank you!!
Suppose the proportion p of defective items in a large population of items is unknown and that it is desired to test the following hypothesis:
Null: p=.2, Alternative: p does not equal .2
Suppose also that a random sample of 20 items is drawn from the population. Let Y denote the number of defective items in the sample, and consider a test procedure delta such that the critical region contains all the outcomes for which either Y is greater than or equal to 7, or Y is less than or equal to 1.
Determine the value of the power function at the points p= 0, .1, .2, .3, .4, .5, .6, .7, .8, .9, and 1 and sketch the power function.
Determine the size of the test.
I had to recall what 'size' meant
According to this, Statistical hypothesis testing - Wikipedia, the free encyclopedia, its just alpha
Well that the probability of rejecting under the null which happens when p=.2
AND while