Binomial Power

#1
Hi,
So we're been working on type 1, type 2 errors and power. I've gotten everything good so far but not I'm stuck on a question on Binomial Power. First of all I can't even find anything in my book that talks about Binomial power or errors. I tried using the binomial probabilities for this question but I can't seem to get it right!
Here is the question:
The caps on pop bottles are not "balanced" since one side is open while the other side is closed. Suppose we want to test whether the closed side lands on the top less often than the open side when it is dropped. Let X = number of times the cap lands with the closed side up in 12 tosses.

We want to test
Ho: p = 0.5
Ha: p = 0.4

We decide to reject Ho if X < 3, that is if less than 3 of the tosses result in the closed side being on top. {You may need to review binomial probabilities for this question.}

(a) Find the probability of a Type I error, that is, the probability that you reject Ho when p = 0.5, i.e. the cap is balanced.

(b) Find the probability of a Type II error for the given alternative.

How would I find type I and type II error using binomial probabilities?
Any help would be greatly appreciated!

Thanks,
Marie Lainesse
 

Dason

Ambassador to the humans
#2
If you know that X is binomial with n = 12 and p = .5 do you know how to find P(X = 0)? P(X = 1)? P(X = 2)?
 
#3
Yes that I do know how to do! I think it's the P=0.5 and P=0.4 thats confuses me! And once I have my final answer from the binomial probability equation, what would I need to do?
 

Dason

Ambassador to the humans
#4
Well the probability of a type I error is the probability that you reject Ho when Ho is actually true. So when p = .5 find P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2). Can you see how you would find the probability of a type II error?
 
#5
Yes! I'm pretty sure! So for a type II error, I would use p=0.4 since we are looking for the probability of accepting Ho when Ha is actually true. Is this right? It would make sense now that I think of it :)