I have the following information:
I know the θ of the population before hand as 0.55. Now I took 200 samples from a Bernoulli distribution Bern(0.55).I have to use this random sample to carry out the large sample Z-test of
H0 : θ = 0.5
Ha : θ > 0.5
If the significance level (α = 0.03) for this test is 3%, how do I compute the approximate probability of a Type II error.
My solution:
As I know that, α = 0.03 the probability of a Type I error = 0.03.
Type II error would occur when we fail to reject H0 when Ha is true. We fail to reject H0 if Z < z 1-α which is pnorm(1-α) = 0.833.
I have the following confusion with my above solution:
- But, shouldn't the Type II error occur only when Ha is true. And the above calculation would result in a large Type II error. So, should I add a conditional probability that when θ > 0.5.
- As I was already told that θ = 0.55, does this make my Ha true. And the Type II error is indeed 0.833 ?