Transcript ppt

Section 10.4.1
Inference as Decision
AP Statistics
March 4, 2010
CASA
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When inference is used to make a
decision…
Either you reject H0 or you fail to reject H0.
 You can reject H0 correctly
 You can fail to reject H0 correctly
 You reject H0 incorrectly

 (Type

I error)
You can fail to reject H0 incorrectly
 (Type
II error)
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Fail to Reject
H0
Reject H0
H0 is true
Correct
Type I error
H0 is false
Type II error
Correct
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Potato Chips Example
The salt content of the chips should have a mean of
2 mg with a standard deviation of .1 mg.
 When deciding whether to accept or reject a batch
of potato chips, a company looks at the salt content
of 50 chips.
 If the salt content is too far away from the mean, it
will reject the batch.

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What range values are acceptable?
The company will check a 50 chip sample.
 If our alpha is .05, the acceptable range is the same
as the 95% confidence interval:

z
*

n
*
z  1.96
0.1
2  1.96
50
2  .0277, 2  .0277
1.9723, 2.0277 
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Accept or reject?

We understand with
normal variation and
everything working
normally, we will get a
sodium value between
1.9723 mg and 2.0277 mg
95% of the time.
0.1
2  1.96
50
2  .0277, 2  .0277
1.9723, 2.0277 
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Accept or reject?

We understand with
normal variation and
everything working
normally, we will get a
sodium value between
1.9723 mg and 2.0277 mg
95% of the time.


This means the 5% of the
time you will reject a batch
of chips that are fine.
When we reject the batch
(and H0) incorrectly we
have committed a Type I
error.
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Accept H0
Reject H0
Reject H0
95% Confidence Interval
1.9723
2.0277
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Significance and Type I Error

The significance level α of any fixed level test is the
probability of a Type I error. That is, α is the
probability that the test will reject the null hypothesis
H0 when H0 is in fact true.
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Probability of reject H0 correctly



The probability that we correctly reject H0 (that is, we say
there is a difference when the difference really exists) is
called the “Power”.
The probability of the Type II error is 1- “Power”
We increase the “Power” by either increasing
 the
sample size
 Alpha

Remember, when we increase alpha, we increase the
probability of the Type I error
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Assignment

10.66-10.69 all
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