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amanning
10-12-2005, 09:48 PM
I know that power is one minus beta...but how do you calculate beta?

quark
10-12-2005, 10:05 PM
Hi amanning,

Beta is the type II error. It's the probability of not rejecting H0 when H0 is false.

To calculate beta, first you need to get the rejection/acceptance region based on your H0, H1 and significance level, then you can get the conditional probability of the acceptance region given H0 is false.

Let me know if you have further questions.

amanning
10-12-2005, 10:11 PM
Ok. The problem I am working on is Let X:N(?, 64)
n=16
H1: m=50
H2: m>50
alpha= >.05
Compute Power for m=56
(m is mew as I don't know how to type in greek)

quark
10-12-2005, 10:15 PM
You want to find the critical value first, then the rejection region, ie reject H0 when sample mean xbar is....

amanning
10-12-2005, 10:18 PM
would this make sense:
-
X= 59.29
Z(59.29)=1.645
Beta=.05
1-Beta=.95

quark
10-12-2005, 10:26 PM
would this make sense:
-
X= 59.29
Z(59.29)=1.645
Beta=.05
1-Beta=.95

It's more complex than that. :)

You have alpha=.05, critical value of 1.645 is correct. Calculate the standard error of the mean, then the critical value is the z-value for the boundary of the rejection region. Rejection region should be Xbar>...

amanning
10-12-2005, 10:36 PM
standard error of the mean:
2
found by taking the square root of the variance (variance 64) which is 8 and dividing it by the square root of the sample (square root of 16) which is 4.

quark
10-12-2005, 10:45 PM
So you would reject H0 if

(Xbar-mu)/se_Xbar > 1.645
(Xbar-50)/2 > 1.645
Xbar >53.29

Next we get power directly by calculating P(Xbar >53.29 | mu=56)

P(Xbar >53.29 | mu=56)
=P[(Xbar-mu)/se_Xbar > (53.29-mu)/se_Xbar | mu=56]
=P[Z > (53.29-56)/2]
=...

You can do the rest. :)

amanning
10-12-2005, 10:47 PM
OK, I guess a better question would be how do I figure out the z score?
I have a 'formula' written down that looks like Z(x)= x-mx/standard error, I don't know what to do with it.

quark
10-12-2005, 10:54 PM
Substitute the values.

P(Xbar >53.29 | mu=56)
=P[(Xbar-mu)/se_Xbar > (53.29-mu)/se_Xbar | mu=56]
=P[Z > (53.29-56)/2]
=P(Z > -1.36)
=P(Z<1.36)
=...

The final answer can be found in the normal table.

amanning
10-12-2005, 11:00 PM
Thank you so much for all of your help. Sometimes I need to see things written differently for them to make sense...

quark
10-12-2005, 11:02 PM
You are welcome. Please pass a good word for us. Thanks.

amanning
10-12-2005, 11:02 PM
In reviewing this I do have one more, most likely annoying question, why in post 8 is it x bar -50/2>1.645 and not x bar-56/2>1.645

quark
10-12-2005, 11:09 PM
Very good question. When you try to find the rejection region, you use the mu in your H0. After you get the region, you use mu=56, notice I've always included the condition mu=56 afterwards. This is a KEY concept in power calculation.

amanning
10-12-2005, 11:15 PM
Oooh. I hadn't noticed, or at least hadn't understood. But that makes sense.
Thanks again...
I'm sure I'll be back...

quark
10-12-2005, 11:25 PM