Question

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You have a normal distribution with σ = 1.

You wish to test the following hypotheses:

H0: μ = 0
Ha: μ > 0

You decide to reject H0 if x > 0.

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

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 a false null hypothesis. 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.