Hypothesis testing

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One- and
Two-Sample
Tests of
Hypotheses

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Definition 10.1

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Section 10.2
Testing a
Statistical
Hypothesis

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Figure 10.1 Decision criterion for
testing p = 0.25 versus p > 0.25

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Definition 10.2

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Definition 10.3

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Table 10.1 Possible Situations for
Testing a Statistical Hypothesis

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Figure 10.2 Probability of a type I
error

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Figure 10.3 Probability of a type II
error

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Figure 10.4 Critical region
(in blue)

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Figure 10.5 Critical Region for
testing m = 68 versus m 68


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Figure 10.6 Probability of type II error
for testing m = 68 versus m = 70

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Figure 10.7 Type II error for testing m
= 68 versus m = 68.5

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Definition 10.4

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Section 10.3
The Use of
P-Values for
Decision Making
in Testing
Hypotheses

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Figure 10.8 Data that are likely
generated from populations having two
different means

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Definition 10.5

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Section 10.4
Single Sample:
Tests Concerning
a Single Mean

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Figure 10.9 Critical region for the
alternative hypothesis 
m m


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Figure 10.10 P-value for Example
10.3

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Figure 10.11 P-value for Example 10.4

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Figure 10.12 MINITAB printout for one
sample t-test for pH meter

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Section 10.5
Two Samples:
Tests on Two
Means

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Table 10.2 Data for Case Study
10.1

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Figure 10.13 SAS printout of paired
t-test for data of Case Study 10.1

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Section 10.6
Choice of Sample
Size for Testing
Means

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Table 10.3 Tests Concerning
Means

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Figure 10.14 Testing m = mo
versus m = mo + d

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Figure 10.15 Testing m1-m2 = do
versus m1-m2 =d + d

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Section 10.7
Graphical
Methods for
Comparing
Means

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Figure 10.16 Two box-and whisker
plots of plasma ascorbic acid in
smokers and nonsmokers

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Figure 10.17 Two box-and-whisker
plots of seedling data

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Figure 10.18 SAS printout for
two-sample t-test

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Section 10.8
One Sample: Test
on a Single
Proportion

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Section 10.9
Two Samples:
Tests on Two
Proportions

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Section 10.10
One- and Two-
Sample Tests
Concerning
Variances

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Figure 10.19 Critical region for the
alternative hypothesis s > 0.9

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Figure 10.20 Critical region for the
alternative hypothesis s s

2 2
1 2

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Section 10.11
Goodness-of-Fit
Test

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Table 10.4 Observed and Expected
Frequencies of 120 Tosses of a Die

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Table 10.5 Observed and Expected
Frequencies of Battery Lives, Assuming
Normality

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Section 10.12
Test for
Independence
(Categorical
Data)

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Table 10.6 2 3 Contingency Table


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Table 10.7 Observes and
Expected Frequencies

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Section 10.13
Test for
Homogeneity

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Table 10.8 Observed Frequencies

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Table 10.9 Observed and
Expected Frequencies

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Table 10.10 k Independent
Binomial Samples

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Table 10.11 Data for Example
10.15

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Table 10.12 Observed and
Expected Frequencies

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Section 10.14
Two-Sample
Case Study

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Table 10.13 Data for Two-
Sample Case Study

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Figure 10.21 Normal quantile-
quantile plot of data for alloy A

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Figure 10.22 Normal quantile-
quantile plot of data for alloy B

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Figure 10.23 Box-and-whisker
plots for both alloys

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Figure 10.24 Annotated SAS
printout for alloy data

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Potential
Misconceptions
and Hazards;
Relationship to
Material in Other
Chapters
Section 10.15