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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 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.]

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Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809
BuyFind

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

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Chapter
Section
Chapter 8, Problem 76SE
Textbook Problem

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 H 0 : σ 2 = σ 0 2 (equivalently, σ = σ0). Then when H0 is true, the test statistic χ2 = (n − 1)S2/ 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 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. [Hint: Consult Table A.11.]

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Chapter 8 Solutions

Probability and Statistics for Engineering and the Sciences
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