E/Stat 265 Fall 2009
IOE/Stat 265, Fall 2009
Lecture #20:
Hypothesis Tests for
One Variance or Proportion
83
Test Population Proportion
Test Normal Variance (or Std Dev)
8X
8.5
Summary of Single Population Tests
1
xample
:
arpet Durability
Example 4: Carpet Durability
arpet Durability data:
urability MPJ
±
Carpet Durability data:
Durability.MPJ
±
Manufacturer Claims average life expectancy
to exceed 10 years.
±
Use Minitab to verify the claim.
2
sing Minitab for Hypothesis Testing
Using Minitab for Hypothesis Testing
3
sing Minitab for Sample Size Planning
Using Minitab for Sample Size Planning
±
Suppose the carpet’s average life expectancy
was actually 11 years.
How much data
ould be required to justify the “10 Year”
would be required to justify the 10 Year
claim with probability .90 ?
(Assume
α
= .05)
4
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View Full Documentingle Sample Proportion Tests
83
Single Sample Proportion Tests
ypically we only conduct proportion hypothesis tests
±
Typically, we only conduct proportion hypothesis tests
for large samples.
±
For small sample size, we may compute probabilities of
Type I and Type II errors using Cumulative Binomial
calculations.
Case
USE
Test Statistic
Formula
Tests of Single Population Proportion
4
Large sample,
normal
z
o
p
o
ˆ
−
5
approxim ation
n
/
)
1
(
−
quivalent Approach
Equivalent Approach
t X = number of sample items with property of
±
Let X = number of sample items with property of
interest
±
Assume Binomial r.v.
With E(X) = np
V(X) = np(1p)
ase
SE
est Statistic
ormula
4
z
o
)
xn
−
−
6
approximation
(1
oo
np
ingle Proportion
arge Sample
Single Proportion  Large Sample
±
Require np
≥
10 and n(1p )
≥
10
(Normal
qp
0
(
p
o
)
(
approximation)
±
Null Hypothesis:
=
o
±
Test Statistic:
ˆ
(1
) /
pp
z
−
=
−
±
Alt Hypothesis
Reject Region
≥
10
:
Hp
α
>≥
<≤
−
7
1
0
/2
or
≠≤
−
≥
xample
:
jection Molding
Example 5: Injection Molding
±
Suppose you produce injection molding parts.
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 Fall '09
 GaryHerrin
 Statistical hypothesis testing, Statistical significance, Type I and type II errors, Statistical vs Statistical vs Practical Significance Significance

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