Chapter 7 presented a CI for the variance s2 of a normal population distribution. The key result there was that the rv has a chi-squared distribution with df. Consider the null hypothesis (equivalently,

). Then when H0 is true, the test statistic has a chi-squared distribution with df. If the relevant alternative is , rejecting H0 if gives a test with significance level a.

To ensure reasonably uniform characteristics for a particular application, it is desired that the true standard deviation of the softening point of a certain type of petroleum pitch be at most

.50°C. The softening points of ten different specimens were determined, yielding a sample standard deviation of .58°C.

Does this strongly contradict the uniformity specification?

Test the appropriate hypotheses using .