80. Chapter 7 presented a CI for the variance 2 of a normal population distribution. The key result there was that the rv 2
(n  1)S2

/2 has a chi-squared distribution with n  1 df. Consider the null hypothesis H0: 2
2 0 (equivalently,
0). Then when H0 is true, the test statistic 2
(n  1) S2

/2 0 has a chi-squared distribution with n  1 df. If the relevant alternative is Ha: 2 2 0, rejecting H0 if (n  1)s2

/2 0  2

,n1 gives a test with significance level . 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 
.01.