Inference Procedures for Two Populations

1
Inference Procedures forTwo Populations
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2
Independent versusDependent Samples

• Independent Samples
• The occurrence of an observation in the first
  sample has no effect on the value(s) in the other
  sample.
• Dependent Samples or paired samples
• The occurrence of an observation in the first
  sample has an impact on the corresponding value
  in the second sample.

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3
(1 - ?) 100Confidence Interval for ?1 - ?2
For large samples where ?s are known
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4
(1 - ?) 100Confidence Interval for ?1 - ?2
For large samples where ?s are unknown
Introduction to Business Statistics, 5e
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5
Sample Sizes
To minimize total sample size
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6
Hypothesis Testing for ?1 and ?2 (Large Samples)
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7
Example 9.2
Define the Hypothesis Ho ?1 ? ?2 (Texgas is
less expensive) Ha ?1 gt ?2 (Quik-Chek is less
expensive)
Define the test statistic
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Define the rejection region (? .05) Reject HO
if Z gt 1.645
Figure 9.4
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Evaluate the test statistic
Because 3.5 gt 1.645 we reject HO
State the conclusion Quik-Chek stores do charge
less for gasoline(on the average) than do
Texgas stations.
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10
Large Sample Tests for ?1 and ?2
Two-Tail Test
Ho ?1 ?2 Ha ?1 ? ?2 Reject HO if Z gt
Z
a
/
2
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11
Large Sample Tests for ?1 and ?2
One-Tail Test
Ho ?1 ? ?2 Ha ?1 gt ?2 Reject Ho if Z gt Z?
Ho ?1 ? ?2 Ha ?1 lt ?2 Reject Ho if Z lt - Z?
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12
(1 - ?) 100 Confidence Interval for ?1 - ?2
(Small Independent Samples)
Introduction to Business Statistics, 5e
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Hypothesis Testing for ?1 - ?2 (Small,
Independent Samples)
Example 9.5
1. Ho ?1 ?2 Ha ?1 ? ?2 2.
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3. Reject HO if t gt t ?/2, df t .05,22
1.717
4.
Because t 3.25 gt 1.717, we reject HO
5. There is a significant difference in the
average blowout times for the two brands
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15
Comparing VariancesAssumptions

• Both populations are normal
• The samples are independent

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Comparing Variances
Introduction to Business Statistics, 5e
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Figure 9.14
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Hypothesis Test for ?1 and ?2
Two-Tail Test
Ho ?1 ?2 Ha ?1 ? ?2
Reject Ho if F gt
F
v
v
?/2
,
,
1
2
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
F
or if F lt
v
v
1-?/2
,
,
1
2
18
Hypothesis Test for ?1 and ?2
One-Tail Test
Ho ?1 ? ?2 Ha ?1 gt ?2
Ho ?1 ? ?2 Ha ?1 lt ?2
Reject Ho if F gt
F
Reject Ho if F gt
F
v
v
v
v
?
,
,
1-?
,
,
1
2
1
2
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19
Confidence Interval for ?12 /?22
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20
Confidence Interval for ?d
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21
Hypothesis Test for ?d
Ho ?d 0 Ha ?d ? 0
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