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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.
You will recall from Chapter 1 that we used the symbol: X to refer to the mean of
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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