Chapter 7 presented a CI for the variance s2 of a normal population distribution. The ke...

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 hypothes is equivalently σ = σ₀, ). Then when H0 is true, the test statistic has a chi-squared distribution with n-1 df. If the relevant alternative is rejecting H₀ if gives a test with significance level α. 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.