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StatisticsProbability and Statistics for Engineering and the SciencesChapter 7 presented a CI for the variance σ 2 of a normal population distribution. The key result there was that the rv χ 2 = (n − 1) S 2 / σ 2 has a chi-squared distribution with n − 1 df. Consider the null hypothesis H 0 : σ 2 = σ 0 2 (equivalently, σ = σ 0 ). Then when H 0 is true, the test statistic χ 2 = ( n − 1) S 2 / σ 0 2 has a chi-squared distribution with n − 1 df. If the relevant alternative is H a : σ 2 > σ 0 2 the P -value is the area under the χ 2 curve with n − 1 df to the right of the calculated χ 2 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. [ Hint : Consult Table A.11.]BuyFind*arrow_forward*

9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

Chapter 8, Problem 76SE

Textbook Problem

Chapter 7 presented a CI for the variance *σ*^{2} of a normal population distribution. The key result there was that the rv *χ*^{2} = (n − 1)*S*^{2}/*σ*^{2} has a chi-squared distribution with *n* − 1 df. Consider the null hypothesis
*σ = σ*_{0}). Then when *H*_{0} is true, the test statistic *χ*^{2} = (*n* − 1)*S*^{2}/
*n* − 1 df. If the relevant alternative is
*P*-value is the area under the *χ*^{2} curve with *n* − 1 df to the right of the calculated *χ*^{2} 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. [*Hint*: Consult Table A.11.]

Probability and Statistics for Engineering and the Sciences

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