Hypothesis Testing

The Alternative Hypothesis as a Research Hypothesis

Many applications of hypothesis testing involve an attempt to gather evidence in support of

a research hypothesis. In these situations, it is often best to begin with the alternative hypothesis

and make it the conclusion that the researcher hopes to support. Consider a particular

automobile that currently attains a fuel efficiency of 24 miles per gallon in city driving.

A product research group has developed a new fuel injection system designed to increase the

miles-per-gallon rating. The group will run controlled tests with the new fuel injection system

looking for statistical support for the conclusion that the new fuel injection system provides

more miles per gallon than the current system.

Several new fuel injection units will be manufactured, installed in test automobiles, and

subjected to research-controlled driving conditions. The sample mean miles per gallon for

these automobiles will be computed and used in a hypothesis test to determine if it can be

concluded that the new system provides more than 24 miles per gallon. In terms of the population

mean miles per gallon , the research hypothesis > 24 becomes the alternative hypothesis.

Since the current system provides an average or mean of 24 miles per gallon, we

will make the tentative assumption that the new system is not any better than the current system

and choose <= 24 as the null hypothesis. The null and alternative hypotheses are:

If the sample results lead to the conclusion to reject H0, the inference can be made that

Ha: > 24 is true. The researchers have the statistical support to state that the new fuel injection

system increases the mean number of miles per gallon. The production of automobiles

with the new fuel injection system should be considered. However, if the sample

results lead to the conclusion that H0 cannot be rejected, the researchers cannot conclude

H0: <= 24

Ha: > 24

that the new fuel injection system is better than the current system. Production of automobiles

with the new fuel injection system on the basis of better gas mileage cannot be justified.

Perhaps more research and further testing can be conducted.

Successful companies stay competitive by developing new products, new methods, new

systems, and the like, that are better than what is currently available. Before adopting something

new, it is desirable to conduct research to determine if there is statistical support for

the conclusion that the new approach is indeed better. In such cases, the research hypothesis

is stated as the alternative hypothesis. For example, a new teaching method is developed

that is believed to be better than the current method. The alternative hypothesis is that the

new method is better. The null hypothesis is that the new method is no better than the old

method. A new sales force bonus plan is developed in an attempt to increase sales. The alternative

hypothesis is that the new bonus plan increases sales. The null hypothesis is that

the new bonus plan does not increase sales. A new drug is developed with the goal of lowering

blood pressure more than an existing drug. The alternative hypothesis is that the new

drug lowers blood pressure more than the existing drug. The null hypothesis is that the new

drug does not provide lower blood pressure than the existing drug. In each case, rejection

of the null hypothesis H0 provides statistical support for the research hypothesis. We will

see many examples of hypothesis tests in research situations such as these throughout this

chapter and in the remainder of the text.