Biostatistics

266 CHAPTER 7 HYPOTHESIS TESTING
do this with an asymmetric sampling distribution such as the chi-square
distribution. In this situation the one-sided p value is reported along with
the direction of the observed departure from the null hypothesis. In fact,
this procedure may be followed in the case of symmetric sampling
distributions. Precedent, however, seems to favor doubling the one-sided
p value when the test is two-sided and involves a symmetric sampling
distribution.
For the present example, then, we may report the p value as follows:
p >:05 (two-sided test). A population variance greater than 600 is
suggested by the sample data, but this hypothesis is not strongly
supportedbythetest.
If the problem is stated in terms of the population standard deviation,
one may square the sample standard deviation and perform the test as
indicated above.
&
One-Sided Tests Although this was an example of a two-sided test, one-sided tests
may also be made by logical modification of the procedure given here.
For H A : s 2 > s 2 0 ; reject H 0 if computed x 2 x 2 1
a
For H A : s 2 < s 2 0 ; reject H 0 if computed x 2 x 2 a
Tests involving a single population variance can be carried out using MINITAB
software. Most other statistical computer programs lack procedures for carrying out these
tests directly. The output from MINITAB, using the data from Example 7.7.1, is shown in
Figure 7.7.2.
Test and CI for One Variance
Statistics
N StDev Variance
16 25.9 671
95% Confidence Intervals
CI for CI for
Method StDev Variance
Standard (19.1, 40.1) (366, 1607)
Tests
Method Chi-Square DF P-Value
Standard 16.77 15 0.666
FIGURE 7.7.2 MINITAB output for the data in Example 7.7.1.