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```Chapter 8
Inferences Based on
a Single Sample
Tests of Hypothesis
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8.1
The Elements of a Test of Hypothesis
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Definition
8- 3
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Definition
8- 4
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Definition
8- 5
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Definition
8- 6
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Figure 8.1 The sampling distribution of x ,
Assuming m = 2,400
8- 7
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Definition
8- 8
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Definition
8- 9
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Figure 8.2 Location of the test statistic for a
test of the hypothesis H0: m = 2,400
8 - 10
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Definition
8 - 11
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Figure 8.3 Location of test statistic when
x = 2,430
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Table 8.1
8 - 13
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Procedure
8 - 14
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Procedure
8 - 15
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8.2
Formulating Hypotheses and Setting Up
the Rejection Region
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Procedure
8 - 17
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Definition
8 - 18
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Definition
8 - 19
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Figure 8.4 Rejection regions corresponding
to one- and two tailed tests
8 - 20
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Table 8.2
8 - 21
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Figure 8.5 Two-tailed rejection region:
a = .01
8 - 22
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8.3
Test of Hypothesis about a Population
Mean: Normal (z) Statistic
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Procedure
8 - 24
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Definition
8 - 25
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Definition
8 - 26
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Table 8.3
8 - 27
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Figure 8.6 MINITAB descriptive statistics for
fill amounts, Example 8.4
8 - 28
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8.4
Observed Significance Levels: p-Values
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Definition
8 - 30
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Figure 8.7 Finding the p-value for an uppertailed test when z = 2.12
8 - 31
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Procedure
8 - 32
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Figure 8.8 Finding the p-value for an onetailed test
8 - 33
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Figure 8.9 Finding the p-value for an twotailed test; p-value = 2(p/2)
8 - 34
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Figure 8.10 SAS test of mean response
time, Example 8.5
8 - 35
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Procedure
8 - 36
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Table 8.4
8 - 37
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Figure 8.11 MINITAB lower-tailed test of
mean LOS, Example 8.6
8 - 38
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Procedure
8 - 39
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Figure SIA8.1 MINITAB test of m = 60 for
KLEENEX survey
8 - 40
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8.5
Test of Hypothesis about a Population
Mean: Student’s t-Statistic
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Figure 8.12 Two-tailed rejection region for
small-sample t-test
8 - 42
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Procedure
8 - 43
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Definition
8 - 44
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Table 8.5
8 - 45
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Figure 8.13 A t-distribution with 9 df and the
rejection region for Example 8.7
8 - 46
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Figure 8.14 MINITAB analysis of 10
emission levels, Example 8.7
8 - 47
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Figure 8.15 The observed significance level
for the test of Example 8.7
8 - 48
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Procedure
8 - 49
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8.6
Large-Sample Test of Hypothesis about a
Population Proportion
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Figure 8.16 Rejection region for breast
cancer example
8 - 51
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Procedure
8 - 52
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Definition
8 - 53
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Figure 8.17 Rejection region for Example
8.9
8 - 54
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Figure 8.18 The observed significance level
for Example 8.10
8 - 55
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Figure 8.19 MINITAB lower-tailed test of p,
Example 8.10
8 - 56
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Figure SIA8.2 MINITAB test of p = .5 for
KLEENEX survey
8 - 57
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8.7
Calculating Type II Error Probabilities:
More about b (Optional)
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Figure 8.20
Values of a and b
for various
values of m
8 - 59
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Procedure
8 - 60
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Procedure (cont’d)
8 - 61
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Procedure
8 - 62
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Procedure (cont’d)
8 - 63
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Definition
8 - 64
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Figure 8.21
Calculation of
b for druginjected rate
(Example 8.11)
8 - 65
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Figure 8.22 MINITAB power analysis for
Example 8.11
8 - 66
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Figure 8.23 Relationship between a, b, and
n
8 - 67
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Definition
8 - 68
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8.8
Test of Hypothesis about a Population
Variance (Optional)
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Table 8.6
8 - 70
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Figure 8.24 Rejection region for Example
8.12
8 - 71
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Figure 8.25 SAS test of fill amount variance,
Example 8.12
8 - 72
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Procedure
8 - 73
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Definition
8 - 74
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