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September 29th, 2016, 03:39 PM   #1
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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...
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September 29th, 2016, 05:17 PM   #2
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Do you know what is meant by Type I and Type II errors?
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September 29th, 2016, 05:19 PM   #3
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Quote:
Originally Posted by arlobear View Post
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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