Type II error textbook question

#1
Hi,

I am currently teaching myself A level statistics from a textbook, which can be difficult when I can't work out how to get from the question to the answer given in the book, so here's hoping you can help!

I keep thinking I've understood the process for type II errors, and then a question comes along that knocks this belief. I've been thinking on the below question for so long that I'm most likely now completely overthinking it, but I'm pretty stuck. It's only the second part of the question, I've got the type I error correct.

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Workings below:
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The answer given is 0.1119, which is 1 - my answer abover, but can't work out why this step in the process would be next?

Thanks, DJW
 

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Dason

Ambassador to the humans
#2
Because you calculated the probability of the statistic falling in the acceptance region. But you want to calculate the probability of rejecting so you really want the probability of being outside the acceptance region.
 
#4
Because you calculated the probability of the statistic falling in the acceptance region. But you want to calculate the probability of rejecting so you really want the probability of being outside the acceptance region.
So I thought that a type II error is the probability of accepting H0 when H0 is false, so from the critical region given, I'd accept H0 when x is within the critical region, so I dont understand why i'd want the probability of rejecting H0 if x <-1.5 or > 1.5, as i thought i'm explicitly looking for the probability of accepting H0, or is this not correct?
 

Dason

Ambassador to the humans
#5
I think you're right. I'm guessing whoever wrote the answer made the same mistake I did and just for some reason thought they read calculate the power or whatever. But I can't see anything wrong with your answer.