My Math Forum Type I and Type II Errors

 September 29th, 2016, 03:39 PM #1 Newbie   Joined: Sep 2016 From: Chicago Posts: 7 Thanks: 0 Type I and Type II Errors Can somebody please explain this to me? It would mean the world! Thanks so much brainiacs! (1) When β is .05, the probability of a Type I error is... (2) When β is .05, the probability of a Type II error is...
 September 29th, 2016, 05:17 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 Math Focus: Yet to find out. Do you know what is meant by Type I and Type II errors?
September 29th, 2016, 05:19 PM   #3
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Quote:
 Originally Posted by arlobear Can somebody please explain this to me? It would mean the world! Thanks so much brainiacs! (1) When β is .05, the probability of a Type I error is... (2) When β is .05, the probability of a Type II error is...
A Type I error is incorrectly declaring H1 when H0 was correct, i.e. a false alarm.

A Type II error is incorrectly declaring H0 when H1 was correct, i.e. a missed detection.

The usual notation is that

$Pr[\text{Type I error}]=\alpha$

$Pr[\text{correct detection}]=\beta \Rightarrow Pr[\text{Type II error}]=1-\beta$

So we can't answer (1) based on the information given.

In (2) $Pr[\text{Type II error}]=1-\beta = 0.95$

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