Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

226 CHAPTER 8 | Introduction to Hypothesis Testing
on the type of research and the type of data, the details of the hypothesis test change
from one research situation to another. In later chapters, we examine different versions of
hypothesis testing that are used for different kinds of research. For now, however, we focus
on the basic elements that are common to all hypothesis tests. To accomplish this general
goal, we will examine a hypothesis test as it applies to the simplest possible situation—
using a sample mean to test a hypothesis about a population mean.
In the six chapters that follow, we consider hypothesis testing in more complex research
situations involving sample means and mean differences. In Chapters 15 and 16, we look
at correlational research and examine how the relationships obtained for sample data are
used to evaluate hypotheses about relationships in the population. Finally, in Chapters 17
and 18, we examine how the proportions that exist in a sample are used to test hypotheses
about the corresponding proportions in the population.
Once again, we introduce hypothesis testing with a situation in which a researcher is
using one sample mean to evaluate a hypothesis about one unknown population mean.
The Unknown Population Figure 8.2 shows the general research situation that we will
use to introduce the process of hypothesis testing. Notice that the researcher begins with
a known population. This is the set of individuals as they exist before treatment. For this
example, we are assuming that the original set of scores forms a normal distribution with
μ = 80 and σ = 20. The purpose of the research is to determine the effect of a treatment
on the individuals in the population. That is, the goal is to determine what happens to the
population after the treatment is administered.
To simplify the hypothesis-testing situation, one basic assumption is made about the
effect of the treatment: if the treatment has any effect, it is simply to add a constant amount
to (or subtract a constant amount from) each individual’s score. You should recall from
Chapters 3 and 4 that adding (or subtracting) a constant changes the mean but does not
change the shape of the population, nor does it change the standard deviation. Thus, we
assume that the population after treatment has the same shape as the original population
and the same standard deviation as the original population. This assumption is incorporated
into the situation shown in Figure 8.2.
Note that the unknown population, after treatment, is the focus of the research question.
Specifically, the purpose of the research is to determine what would happen if the treatment
were administered to every individual in the population.
The Sample in the Research Study The goal of the hypothesis test is to determine
whether the treatment has any effect on the individuals in the population (see Figure 8.2).
Usually, however, we cannot administer the treatment to the entire population so the actual
research study is conducted using a sample. Figure 8.3 shows the structure of the research
FIGURE 8.2
The basic research situation
for hypothesis testing. It is
assumed that the parameter
μ is known for the population
before treatment. The
purpose of the study is
to determine whether the
treatment has an effect on
the population mean.
Known population
before treatment
s 5 20
m 5 80
T
r
e
a
t
m
e
n
t
Unknown population
after treatment
m 5 ?
s 5 20