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The beginning of a study is formed by a question . This question
usually defines the population (or populations) of interest. If
we knew the population then we could answer the question. Often we rephrase
the question in terms of hypotheses. The one hypothesis often reflects
the current state (standard, no change) while a second hypothesis reflects
change. The first hypothesis is refereed to as the null hypothesis and
is denoted by H_{0} , while the second hypothesis is designated
as the alternative hypothesis and is denoted by H_{A} .
In this chapter we are concerned with two populations. For these problems,
there is a natural null hypothesis, namely, that the two populations are
the same. Consider the following questions for two population problems
along with associated hypotheses.
 1.
 At a pharmaceutical company, a new drug has been developed which should
reduce cholesterol much more than their current drug on the market. Is
this true? Hypotheses:

H_{0}: New drug has the same effect on cholesterol as the
current drug.

H_{A}: New drug reduces cholesterol more than the current
drug.
 2.
 A new method for teaching statistics utilizing technology has been developed.
Is it more successful than the usual lecture approach? Hypotheses:

H_{0}: The teaching methods are equally as effective.

H_{A}: The new teaching method is more successful than the
usual approach.
 3.
 Based on head sizes (maximum head breadths), are the ancient Etruscans different
from modern Italians? Hypotheses:

H_{0}: Typical head sizes of Etruscans and Italians are
the same.

H_{A}: Head sizes of Etruscans and Italians differ.
 4.
 A new variety of wheat is developed which should yield more wheat per acre
than a current popular variety.

H_{o}: Yields of the two wheat varieties are about the same.

H_{A}: The yields of the new variety of wheat are larger
than the current popular variety.
It is easy to think of many such examples because we make many comparisons
daily . The only new stuff is the labeling of the hypotheses. Each of the
alternative hypotheses are of the form: (a) one population is better (bigger,
larger) than the other. There are two other classes of alternatives: (b)
one population is worse than the other (actually this is the same as the
other is better) and (c) the populations are different. We will just consider
(a) for a while and discuss the others later.
In life, we must often decide between conflicting claims and usually
we
must decide in the face of uncertainty. We will never be sure which
hypothesis is correct but perhaps we can have some confidence, never 100%,
that our decision is correct.
Next: A Testing Procedure
Up: Tests of Hypotheses
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