Question

If you repeated a hypothesis test 500 times (in other words, 500 different samples from the same population), how many times would you expect to commit a Type I error, assuming the null hypothesis were true: (a) α = .05; (b) α = .01 ?

Answer 1

Solution:

Given: a hypothesis test is repeated 500 times.

We have to determine  how many times would you expect to commit a Type I error, assuming the null hypothesis were true.

Type I Error is rejecting null hypothesis in fact null hypothesis is true and its probability is given by specifying level of significance $\alpha.$

That is:

a P(Type I Error)

Part a) $\alpha = P( Type\: \: I \: Error) = 0.05$

If probability of type I error is 0.05 and  a hypothesis test is repeated 500 times , then we would expect: 0.05 X 500 = 25 times that we commit a Type I error.

Part b)

aP(Type I Error) = 0.01

If probability of type I error is 0.01 and  a hypothesis test is repeated 500 times , then we would expect: 0.01 X 500 = 5 times that we commit a Type I error.