How do you calculate Type 1 error and Type 2 error probabilities?

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Answer 1 · 2017-12-09T10:36:44

Type #1# = # P#( Rejecting # H_0# | #H_0# True)
Type #2# = #P#( Accept #H_0# | #H_0# False )

Null Hypothesis: #H_0 : mu = mu_0#
Alternative Hypothesis: #H_1: mu<,>, != mu_0#

Type 1 errors in hypothesis testing is when you reject the null hypothesis #H_0# but in reality it is true

Type 2 errors in hypothesis testing is when you Accept the null hypothesis #H_0# but in reality it is false

We can use the idea of:

Probability of event #alpha # happening, given that #beta# has occured:

#P(alpha|beta) =( P(alphannbeta))/(P(beta)) #

So applying this idea to the Type 1 and Type 2 errors of hypothesis testing:

Type #1# = # P#( Rejecting # H_0# | #H_0# True)
Type #2# = #P#( Accept #H_0# | #H_0# False )