Computing Power

#2
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.
 
#3
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)
 
#6
amanning said:
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>...
 
#7
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.
 
#8
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. :)
 
#9
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.
 
#10
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.
 
#14
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.