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3.2.1 Hypotheses Always Refer to the Population of People,

Plants, or Animals that You Are Studying

The ﬁrst step is to understand that our hypotheses always refer to the
population
of

people, plants, or animals under study.

For example, if we are interested in studying a species of noxious weed found

along highways of southern South Dakota, we would select various sections of

highways and estimate the number of weeds found in these sections, these sections

would be used as our sample. This sample would be used in generalizing our

ﬁndings for all of the highways in southern South Dakota.

All of the highways in southern south Dakota would be the
population
that we

are interested in studying, while the particular sections of highways in our study are

called the
sample
from this population.

Since our sample sizes typically contain only a portion of the highways, we are

interested in the results of our sample
only insofar as the results of our sample can

be “generalized” to the population in which we are really interested.

That is why our hypotheses always refer to the population, and never to the

sample of people, plants, animals, or events in our study.

the sample we use in our research study (See Section 1.1).

We will use the symbol:

(the Greek letter “mu”) to refer to the population

m

mean.

In testing our hypotheses, we are trying to decide which one of two competing

hypotheses about the population mean we should accept given our data set.

3.2.2 The Null Hypothesis and the Research (Alternative)

Hypothesis

These two hypotheses are called the
null hypothesis
and the
research hypothesis.

Statistics textbooks typically refer to the
null hypothesis
with the notation:
H
0
.

The
research hypothesis
is typically referred to with the notation:
H
1
, and it is

sometimes called the
alternative hypothesis
.

Let’s explain ﬁrst what is meant by the null hypothesis and the research

hypothesis:

1.
The null hypothesis is what we accept as true unless we have compelling

evidence that it is not true.

2. The research hypothesis is what we accept as true whenever we reject the null

hypothesis as true.

This is similar to our legal system in America where we assume that a supposed

criminal is innocent until he or she is proven guilty in the eyes of a jury. Our null

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