# Thread: Probability of a Type I Error

1. ## Probability of a Type I Error

I'm finding it difficult to solve this question, looking for some help:

Suppose we want to test H0: μ = 50 against Ha: μ > 50, at a significance level of α = 0.0505 based on a random sample of 40. What is the probability of a type II error when μ = 52 and s = 4.
I know how to do a statistic test, but to do that I would need x-bar

I also know that a Type 2 Error is when you accept H0 when it is, in fact, false. So would this probability be the rejection region, on the right-tailed normal distribution chart? If so, how would I find it?

Also, I know that α = 0.0505 translates to z < 1.64

2. ## Re: Probability of a Type I Error

You seem to be mixing terms up here.

Your post title is "probability of a type I error", but the question you have quoted says "probability of a type II error". You then go on to describe a type 1 error.

For avoidance of ambiguity (source: wikipedia):
Type 1 Error: The probability of rejecting H0 when it is in fact true, ie the chance of being in the rejection region when H0 is true...by definition this is equal to $\alpha$

Type 2 Error: The probability of retaining H0 when it is in fact false, ie the chance of being in the acceptance region when H0 is false...i dont know any way to deduce this from the information you posted in the question.