Chapter 9: Introduction to Hypothesis Testing

378 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING
In another example, suppose the Agri-Seed Company has developed a new fertilizer for
commercial farming. Agri-Seed would introduce this product on the market only if it provides
yields superior to its current fertilizer product. Experience shows that when the current fertilizer
is used to grow sugar beets, a mean yield of 30 tons per acre is expected. To test the new
fertilizer, Agri-Seed researchers will set up the following null and alternative hypotheses:
H 0
: 30 tons
H A
: 30 tons (research hypothesis)
The alternative hypothesis is the research hypothesis. If the null hypothesis is rejected, then
Agri-Seed will have statistical evidence to show that the new fertilizer is superior to the
existing product.
Testing a Claim About the Population Analyzing claims using hypothesis tests can be
complicated because the benefit of the doubt goes to the null hypothesis. Sometimes you
will want to give the benefit of the doubt to the claim, but in other instances you will be
skeptical about the claim and will want to place the burden of proof on the claim. For consistency
purposes, the rule adopted in this text is that if the claim contains the equality, the
claim goes in the null. If the claim does not contain the equality, it goes in the alternative.
A recent radio commercial has stated the average waiting time at a medical clinic is
less than 15 minutes. A claim like this can be tested using hypothesis testing. The null and
alternative hypotheses should be formulated such that one contains the claim and the other
reflects the opposite position. Since the claim does not contain the equality ( 15), the
claim should be the alternative hypothesis. The appropriate null and alternative hypotheses
are, then, as follows:
H 0
: 15
H A
: 15 (claim)
In cases like this where the claim corresponds to the alternative hypothesis, the burden
of proof is on the medical clinic. If the sample mean is “substantially” less than 15 minutes,
the null hypothesis would be rejected and the alternative hypothesis (and the claim)
would be accepted. Otherwise, the null hypothesis would not be rejected and the claim
could not be accepted.
SUMMARY Formulating the Null and Alternative Hypotheses
1. The null and alternative hypotheses must be stated
in terms of the population of interest (e.g., , ,
or ).
2. If the application involves a test of the status quo,
the status quo forms the null hypothesis and the
burden of proof is to show that the status quo has
changed.
3. If the application involves a research issue, the research
hypothesis forms the alternative hypothesis.
4. If a claim has been made about the population parameter,
the decision maker must determine if he or she is
inclined to agree with the claim before gathering any
data. If so, the claim establishes the null hypothesis;
otherwise, it forms the alternative hypothesis.
EXAMPLE 9-1 Formulating the Null and Alternative Hypotheses
CHAPTER OUTCOMES #1
TRY PROBLEM 9.13
Student Work Hours In today’s economy, university students often work many
hours to help pay for the high costs of a college education. Suppose a university in the
Midwest is considering changing its class schedule to accommodate students working
long hours. The registrar has stated a change is needed because the mean number of