Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Textbook Question
Chapter 10.2, Problem 16E
Reconsider the axial stiffness data given in Exercise 8. ANOVA output from Minitab follows:
| Analysis of Variance for Stiffness | |||||
| Source | DF | SS | MS | F | P |
| Length | 4 | 43993 | 10998 | 10.48 | 0.000 |
| Error | 30 | 31475 | 1049 | ||
| Total | 34 | 75468 | |||
| Level | N | Mean | StDev | ||
| 4 | 7 | 333 .21 | 36.59 | ||
| 6 | 7 | 368.06 | 28.57 | ||
| 8 | 7 | 375.13 | 20.83 | ||
| 10 | 7 | 407 .36 | 44 .51 | ||
| 12 | 7 | 437.17 | 26.00 | ||
| Pooled StDev = 32.3 9 | |||||
Tukey’s pairwise comparisons
Family error rate = 0.0500
Individual error rate = 0.00693
Critical value = 4.10
Intervals for (column level mean) – (row level mean)
| 4 | 6 | 8 | 10 | |
| 6 | -85. 0 | |||
| 15.4 | ||||
| 8 | -92.1 | -57.3 | ||
| 8.3 | 43.1 | |||
| 10 | -124.3 | -89. 5 | -82.4 | |
| -23. 9 | 10. 9 | 18 . 0 | ||
| 12 | -154.2 | -119.3 | -112.2 | -80.0 |
| -53. 8 | -18. 9 | -11. 8 | 20.4 |
a. Is it plausible that the variances of the five axial stiffness index distributions are identical? Explain.
b. Use the output (without reference to our F table) to test the relevant hypotheses.
c. Use the Tukey intervals given in the output to determine which means differ, and construct the corresponding underscoring pattern.
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A wine enthusiast named Suds collected data on the alc content (percent by volume) of wine for one grape variety in 2012 by a random sample of winemakers in Italy. Suds created the following Table:
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Use the table to determine whether mean alc content of all wines for that grape in 2012 in Italy was greater than 12.75% at the 0.1 significance.
a) State the null and alternaternative hypothesis.
b) What is the calculated value of the associated test statistic and what is the critical value of the associated test statistic?
c) State your decision about the null hypothesis by comparing calculated and critical values of the statistic. State your conclusion(describe what the decision means in this problem).
The valve pressure was tested on 250 engines and the mean pressure was 5.9 lbs/square inch. Assume the variance is known to be 0.36. If the valve was designed to produce a mean pressure of 5.8 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs about the specifications?
Given the following ANOVA table, calculate the F-ratio and the F critical values.
ANOVA for Regression
Source
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10
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F- ratio = 2.41; F critical = 3.71
O F- ratio = 14.65; F critical = 4.76
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Chapter 10 Solutions
Probability and Statistics for Engineering and the Sciences
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