# Statistics - Power

• Jan 2nd 2013, 05:24 AM
emme1
Statistics - Power
Hi,
I have some problem with understanding the meaning of power. I would be more then happy if someone could help me explain this problem below.

A manufacturing process wants the proportion of defective units to be as highest 10%.
Select 100 units from a large portion. If 14 or more units are defected they will adjust the process, they consider that they have evidence that the proportion of defective units is more than 10%.
Ho: π= 0,10
rejection area x>14, X=number of defective units

a) Decide the test, significance level
b) What is the power of the test if the proportion of defected units from the large proportions is 15%

Thanks!
Emma
• Jan 2nd 2013, 02:54 PM
chiro
Re: Statistics - Power
Hey emme1.

This is a good resource:

Statistical power - Wikipedia, the free encyclopedia

Think about power is the ability to handle the situation when H0 is rejected when it should be.

In hypothesis testing you have two errors and the other scenario when you accept the right hypothesis.

A test with good statistical power will reject H0 when it needs to be rejected with higher probability and minimize those other errors.

You can never get rid of the errors, but you can do your best to minimize them in the best way possible both with statistical theory and with practical techniques that involve sampling protocols as well as experimental design and survey analyses.
• Jan 3rd 2013, 05:16 AM
emme1
Re: Statistics - Power
Thanks Chiro.
Ok, I do understand power but I cant figure out how to solve the problem above.
Maybe you know :) ?
• Jan 3rd 2013, 05:23 AM
abender
Re: Statistics - Power
$H_0\colon \pi=0.10$
$H_a\colon \pi>0.10$

Rejection Region: $X\geq14$

$\alpha = P\left(\text{Reject }H_0 | H_0\text{ is true}\right) = P\left(X\geq14 | \pi=0.10\right)$
• Jan 3rd 2013, 05:53 AM
emme1
Re: Statistics - Power
Thank you!

so..

z=(0,14-0,10)/√(0,1*0,9)/100) = 1,33
and that gives 0,4082 (from the z - table)
0,4082+0,5 = 0,9081
1-0,9082= 0,0918 Alpha= 0,0918??
Im right? And now what about the power? :)
• Jan 3rd 2013, 05:54 AM
abender
Re: Statistics - Power
I believe so.
• Jan 3rd 2013, 06:00 AM
emme1
Re: Statistics - Power
how do I solve the power?
• Jan 3rd 2013, 06:06 AM
abender
Re: Statistics - Power
Quote:

Originally Posted by emme1
Thank you!

so..

z=(0,14-0,10)/√(0,1*0,9)/100) = 1,33
and that gives 0,4082 (from the z - table)
0,4082+0,5 = 0,9081
1-0,9082= 0,0918 Alpha= 0,0918??
Im right? And now what about the power? :)

Power is the probability of rejecting the null hypothesis when it is false. That is, one minus the probability of a Type II error.
• Jan 3rd 2013, 06:13 AM
emme1
Re: Statistics - Power
1-β = power, I know
So in this cause:
z=(0,14-0,15)/√(0,15*0,85)/100) = -0,28
and that gives 0,1103 (from the z - table)
0,1103+0,5=0,6103
0,6103 is typ II error?
Im confused.

• Jan 3rd 2013, 12:08 PM
abender
Re: Statistics - Power
Quote:

Originally Posted by emme1
1-β = power, I know
So in this cause:
z=(0,14-0,15)/√(0,15*0,85)/100) = -0,28
and that gives 0,1103 (from the z - table)
0,1103+0,5=0,6103
0,6103 is typ II error? -- wrong here. 1 - 0.6103 is the probability of a Type II error.
Im confused.