Chapter 7 presented a CI for the variance 2 of a normal population distribution. The key result

Chapter 7 presented a CI for the variance σ2 of a normal population distribution. The key result there was that the rv χ2 = (n - 1)S2/σ2 has a chi-squared distribution with n - 1 df. Consider the null hypothesis H0: σ2 = σ02 (equivalently, σ = σ0). Then when H0 is true, the test statistic χ2 = (n - 1)S2/σ02 has a chi-squared distribution with n - 1 df. If the relevant alternative is Ha: σ2 > σ02 the P-value is the area under the χ2 curve with n - 1 df to the right of the calculated χ2 value. 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 α = .01.