Chapter 7 presented a CI for the variance 2 of a normal

Chapter 8, Problem 8.80

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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 .50C. The softening points of ten different specimens were determined, yielding a sample standard deviation of .58C. Does this strongly contradict the uniformity specification? Test the appropriate hypotheses using .01. 81. Refer