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7.7 HYPOTHESIS TESTING: A SINGLE POPULATION VARIANCE 267
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 7 .05 (two-sided test). A population variance greater than
600 is suggested by the sample data, but this hypothesis is not strongly
supported by the test.
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.
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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 7 s 2 0, reject H 0 if computed x 2 Ú x 2 1-a
For H A : s 2 6 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.