Power of a Test
Remember:

Type I error – Reject the H0 when you
shouldn’t have.

Type II error - Fail to reject the Ho
you should have.
when
Fill in the chart with the type of error
Null is True
Null is False
Reject Null
Fail to Reject Null
By choosing a level of significance (  ) we determine
the probability of committing a type I error.
Power of a Test:
(1 – β)

It measures the sensitivity of the test to detect a real
difference in parameters if one really exists.

Rejecting a False Ho.

To increase the power of a test we


Increase alpha
Use a larger sample size.
Null is True
Null is False
Reject Null
Type I error (α)
Correct decision
(1-β)
Fail to Reject Null
Correct decision
(1-α)
Type II error (β)
Cigarette manufacturer claims that the mean nicotine content
of its cigarettes is 1.5 mg. Researchers believe it’s more than
this. Test a sample of 36 and find standard deviation is 0.2.
Use a 1% significance level. (Suppose it’s really 1.6)
A study claims that the mean weight of a book is 2.4 pounds.
Researchers believe that it is more. Test a sample of 30 and
st. dev. Is 0.5 pounds. Use 5% significance level. (What if it’s
really 2.7 pounds?)
A study claims that the mean weight of a dog is 26.8
pounds. Researchers believe that it’s less than this. Test a
sample of 36 and st. dev. Is 2.2 pounds. Use 5% significance
level. (What if it’s really 26 pounds?)
Homework

Worksheet