Re: Type II Error (Help me!!!)

Thanks for the comments. Since it has caused a little controversy, I
probably did not do the best job of "summarizing" the problem. But I think
I get it now. But for the record:

29: Refer to Exercise 20, Calculate the value of Beta for the alternative
p_a=.15.

20: A manufacturer claimed that at least 20% of the public preferred her
product. A sample of 100 persons is taken to check her claim. Whith alpha
= .05, how small would the sample percentage have to be before the claim
could legitamately be refuted? (Notice that this would involve a one-tailed
test of the hypothesis).

OK, so admittedly, I did not do the best job communicating this problem
without the book. Sorry about that. (I guess I was being lazy and didn't
want to go get the book, which I had to anyway so I guess that shows me).

Now that I read the "refuted" part I see that I have indeed calculated the
wrong extreme (thanks Richard Ulrich). So instead of (.2 +.0658) I need
(.2 - .0658 = .1342).

A curious thing happens now, the formula in the book does give me the
z-score I was looking for.

(.1342 - .15)/(SqRt[(.15)*(.85)/100]) = -.442

Low and behold,
P (Z>-.44) = .67

It is hard for me to believe that after all the time I spent checking
formulas with different values I didn't once check nor question that I had
calculated the wrong extreme. Thanks for the help everybody. Once again,
sorry for not posting the problem "word for word" in my original post. I
will be sure not to make that mistake again.

I'm Not Worthy.


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