Hypothesis power ?

#1
mu=78
population std deviation=12
Normal Distribution
n=16
alpha level=.05

* compute the power of the hypothesis test if the program has a 3-point effect.
I came up with 83.88 %

[ i got this by mulitiping the z-core of 1.96+(78)*2
then i found the propotion which was .08388*10=83.88%


* compute the power of the hypothesis test if the program has a 6-point effect.


I looked at the example in the book and I'm just not understanding! Help. Thanks.
 

Dragan

Super Moderator
#2
mu=78
population std deviation=12
Normal Distribution
n=16
alpha level=.05

* compute the power of the hypothesis test if the program has a 3-point effect.
I came up with 83.88 %]

[ i got this by mulitiping the z-core of 1.96+(78)*2
then i found the propotion which was .08388*10=83.88%

Based on your critical value of 1.96 and alpha level (0.05), one important area that you're missing, in terms of computing power, is that you have to consider both sides of the standard normal pdf. In short, the null hyposthesis is two sided.

The other thing you have incorrect is that you have to multiply the z-score by the standard error (12/Sqrt[N]) and then add Mu.

Continue working.
 
#3
I don't know if I have the correct z-score either. How would I know what the z-score would be? I choose 1.96 because the alpha level is .05, is that correct?

The standard error=3

12/sqrt(16)=12/4=3+78=81

So, is 81 the the power of the hypothesis test if the program has a 3-point effect?

Thanks so much for your help! I hope you reply back to give me some feedback on my answer.
 

Dragan

Super Moderator
#4
I don't know if I have the correct z-score either. How would I know what the z-score would be? I choose 1.96 because the alpha level is .05, is that correct?
QUOTE]

A z-score of + - 1.96 is appropriate if your considering a non-directional test with an alpha level of 0.05.

On the other hand, if your considering a directional test, then the appropriate z-score is + - 1.6445 with an alpah level of 0.05.

You can't go any further than this in terms of calculating power until you have decided what the alternative hypothesis is...

Note: Power can only take values between values of 0 and 1, Mkay.