Chapter 9: Introduction to Hypothesis Testing

414 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING
As you now know, hypothesis tests are subject to error. The two potential statistical
errors are
Type I (rejecting a true null hypothesis)
Type II (“accepting” a false null hypothesis)
In most business applications, there are adverse consequences associated with each type of
error. In some cases, the errors can mean dollar costs to a company. For instance, suppose
a health insurance company is planning to set its premium rates based on a hypothesized
mean annual claims amount per participant as follows:
H 0
: $1,700
H A
: $1,700
If the company tests the hypothesis and “accepts” the null, it will institute the planned premium
rate structure. However, if a Type II error is committed, the actual average claim will
exceed $1,700 and the company will incur unexpected payouts and will suffer reduced
profits. On the other hand, if the company rejects the null hypothesis, it will probably
increase its premium rates. But if a Type I error is committed, there would be no justification
for the rate increase and the company may not be competitive in the marketplace and
could lose customers.
In other cases, the costs associated with either a Type I or a Type II error may be even
more serious. If a drug company’s hypothesis tests for a new drug incorrectly conclude that
the drug is safe when in fact it is not (Type I error), the company’s customers may become
ill or even die as a result. You might refer to recent reports dealing with pain medications
such as Vicodin. On the other hand, a Type II error would mean that a potentially useful
and safe drug would most likely not be made available to people who need it if the hypothesis
tests incorrectly determined that the drug was not safe.
In the U.S. legal system where a defendant is hypothesized to be innocent, a Type I
error by a jury would result in a conviction of an innocent person. DNA evidence has
recently resulted in a number of convicted people being set free. A case in point is Hubert
Geralds, who was convicted of killing Rhonda King in 1994 in the state of Illinois.
However, Type II errors in our court system result in guilty people being set free to potentially
commit other crimes.
The bottom line is that as a decision maker using hypothesis testing, you need to be
aware of the potential costs associated with both Type I and Type II statistical errors and
conduct your tests accordingly.
Power
The probability that the hypothesis
test will reject the null hypothesis
when the null hypothesis is false.
Power of the Test
In the previous examples, we have been concerned about the chance of making a Type II
error. We would like beta to be as small as possible. If the null hypothesis is false, we want
to reject it. Another way to look at this is that we would like the hypothesis test to have a
high probability of rejecting a false null hypothesis. This concept is expressed by what is
called the power of the test. When the alternative hypothesis is true, the power of the test
is computed using Equation 9.5.
Power
Power 1 β (9.5)
Refer again to the business application involving the American Lighting Company.
Beta calculations were presented in Figure 9.9, 9.10, and 9.11. For example, in Figure 9.9,
the company was interested in the probability of a Type II error if the “true” population