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9-1 HYPOTHESIS TESTING 287

company. The bottler wants to be sure that the bottles meet the specification on mean internal
pressure or bursting strength, which for 10-ounce bottles is a minimum strength of 200 psi.
The bottler has decided to formulate the decision procedure for a specific lot of bottles as a
hypothesis testing problem. There are two possible formulations for this problem, either

H : 200 psi
0
H : 200 psi (9-5)
1
or

H : 200 psi
0
H : 200 psi (9-6)
1
Consider the formulation in Equation 9-5. If the null hypothesis is rejected, the bottles will be
judged satisfactory; if H 0 is not rejected, the implication is that the bottles do not conform to
specifications and should not be used. Because rejecting H 0 is a strong conclusion, this for-
mulation forces the bottle manufacturer to “demonstrate” that the mean bursting strength of
the bottles exceeds the specification. Now consider the formulation in Equation 9-6. In this
situation, the bottles will be judged satisfactory unless H 0 is rejected. That is, we conclude that
the bottles are satisfactory unless there is strong evidence to the contrary.
Which formulation is correct, the one of Equation 9-5 or Equation 9-6? The answer is it
depends. For Equation 9-5, there is some probability that H 0 will not be rejected (i.e., we
would decide that the bottles are not satisfactory), even though the true mean is slightly
greater than 200 psi. This formulation implies that we want the bottle manufacturer to demon-
strate that the product meets or exceeds our specifications. Such a formulation could be
appropriate if the manufacturer has experienced difficulty in meeting specifications in the past
or if product safety considerations force us to hold tightly to the 200 psi specification. On the
other hand, for the formulation of Equation 9-6 there is some probability that H 0 will be ac-
cepted and the bottles judged satisfactory, even though the true mean is slightly less than
200 psi. We would conclude that the bottles are unsatisfactory only when there is strong evi-
dence that the mean does not exceed 200 psi, that is, when H : 200 psi is rejected. This
0
formulation assumes that we are relatively happy with the bottle manufacturer’s past per-
formance and that small deviations from the specification of 200 psi are not harmful.
In formulating one-sided alternative hypotheses, we should remember that rejecting H is
0
always a strong conclusion. Consequently, we should put the statement about which it is im-
portant to make a strong conclusion in the alternative hypothesis. In real-world problems, this
will often depend on our point of view and experience with the situation.

9-1.4 General Procedure for Hypothesis Tests

This chapter develops hypothesis-testing procedures for many practical problems. Use of the
following sequence of steps in applying hypothesis-testing methodology is recommended.
1. From the problem context, identify the parameter of interest.
2. State the null hypothesis, H 0 .
3. Specify an appropriate alternative hypothesis, H 1 .
4. Choose a significance level .