88. Chapter 8 presented a CI for the variance s2 of a normal population distribution. The key result therewas that the rv has a chi-squared distribution with n1 df. Consider the null hypothesis H0: s2 (equivalently, ss0). Then when H0 is true, the test statistic has a chi-squared distribution with n  1 df. If the relevant alternative is Ha: s2

, rejecting H0 if gives a test with signi cance 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 .50C. The softening points of ten different specimens were determined, yielding a sample standard deviation of

.58C. Does this strongly contradict the uniformity speci cation? Test the appropriate hypotheses using a  .01.