Introduction

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 H₀ , 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:

• H₀: 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:

• H₀: 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:

• H₀: 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.