ch08 - blu03683_ch08.qxd 04:22 PM Page 391 CHAPTE R 8...

Objectives
After completing this chapter, you should be able to
1
Understand the definitions used in hypothesis
testing.
2
State the null and alternative hypotheses.
3
Find critical values for the z test.
4
State the five steps used in hypothesis testing.
5
Test means for large samples, using the z test.
6 Test means for small samples, using the t test.
7
Test proportions, using the z test.
8
Test variances or standard deviations, using
the chi-square test.
9
Test hypotheses, using confidence intervals.
10
Explain the relationship between type I and
type II errors and the power of a test.
Outline
8–1 Introduction
8–2 Steps in Hypothesis Testing—Traditional
Method
8–3 z Test for a Mean
8–4 t Test for a Mean
8–5 z Test for a Proportion
8–6 X
2
Test for a Variance or Standard Deviation
8–7 Additional Topics Regarding Hypothesis
Testing
8–8 Summary
8–1
8
8
Hypothesis Testing
C H A P T E R

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Chapter 8 Hypothesis Testing
8–2
Statistics
Today
How Much Better Is Better?
Suppose a school superintendent reads an article which states that the overall mean score
for the SAT is 910. Furthermore, suppose that, for a sample of students, the average of the
SAT scores in the superintendent’s school district is 960. Can the superintendent conclude
that the students in his school district scored higher than average? At first glance, you
might be inclined to say yes, since 960 is higher than 910. But recall that the means of
samples vary about the population mean when samples are selected from a specific pop-
ulation. So the question arises, Is there a real difference in the means, or is the difference
simply due to chance (i.e., sampling error)? In this chapter, you will learn how to answer
that question by using statistics that explain hypothesis testing. See Statistics Today—
Revisited for the answer. In this chapter, you will learn how to answer many questions of
this type by using statistics that are explained in the theory of hypothesis testing.
8–1 Introduction
Researchers are interested in answering many types of questions. For example, a scien-
tist might want to know whether the earth is warming up. A physician might want to
know whether a new medication will lower a person’s blood pressure. An educator might
wish to see whether a new teaching technique is better than a traditional one. A retail
merchant might want to know whether the public prefers a certain color in a new line of
fashion. Automobile manufacturers are interested in determining whether seat belts will
reduce the severity of injuries caused by accidents. These types of questions can be
addressed through statistical hypothesis testing, which is a decision-making process for
evaluating claims about a population. In hypothesis testing, the researcher must define
the population under study, state the particular hypotheses that will be investigated, give
the significance level, select a sample from the population, collect the data, perform the
calculations required for the statistical test, and reach a conclusion.