Question

You have an SRS of size n = 9 from a normal distribution with σ = 1.

You wish to test:

H0: μ = 0
Ha: μ > 0

You decide to reject Ha if x > 0 and to accept H0 otherwise.

a) Find the probability of a Type I error.
b) Describe a Type II error.

Answer 1

a)

The probability of type I error is 0.5

b)

Type II error is an error committed when we fail to reject the null hypothesis when actually it is false. The probability of Type II error is beta and 1 -beta gives the power of a test.

Explanation:

The probability of a Type I error is the probability of rejecting the null hypothesis when it is actually true. In this case;

pr(x>0 / mu =0)

If the mean is 0 and sigma 1 then x has the standard normal distribution. Now, if x has the standard normal distribution then pr(x>0) = 0.5 since the standard normal distribution curve is symmetric about the mean which in this case is 0.