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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 10.2, Problem 15E

Chapter 10.2, Problem 17E

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Chapter 10 Solutions

Probability and Statistics for Engineering and the Sciences

Ch. 10.1 - In an experiment to compare the tensile strengths...Ch. 10.1 - Suppose that the compression-strength observations...Ch. 10.1 - The lumen output was determined for each of I = 3...Ch. 10.1 - It is common practice in many countries to destroy...Ch. 10.1 - Consider the following summary data on the modulus...Ch. 10.1 - The article Origin of Precambrian Iron Formations...Ch. 10.1 - An experiment was carried out to compare...Ch. 10.1 - A study of the properties of metal plate-connected...Ch. 10.1 - Six samples of each of four types of cereal grain...Ch. 10.1 - In single-factor ANOVA with I treatments and J...

Ch. 10.2 - An experiment to compare the spreading rates of...Ch. 10.2 - In Exercise 11, suppose x3. = 427.5. Now which...Ch. 10.2 - Prob. 13E Ch. 10.2 - Use Tukeys procedure on the data in Example 10.3...Ch. 10.2 - Exercise 10.7 described an experiment in which 26...Ch. 10.2 - Reconsider the axial stiffness data given in...Ch. 10.2 - Prob. 17E Ch. 10.2 - Consider the accompanying data on plant growth...Ch. 10.2 - Prob. 19E Ch. 10.2 - Refer to Exercise 19 and suppose x1 = 10, x2 = 15,...Ch. 10.2 - The article The Effect of Enzyme Inducing Agents...Ch. 10.3 - The following data refers to yield of tomatoes...Ch. 10.3 - Apply the modified Tukeys method to the data in...Ch. 10.3 - The accompanying summary data on skeletal-muscle...Ch. 10.3 - Lipids provide much of the dietary energy in the...Ch. 10.3 - Samples of six different brands of diet/imitation...Ch. 10.3 - Although tea is the worlds most widely consumed...Ch. 10.3 - For a single-factor ANOVA with sample sizes Ji(i =...Ch. 10.3 - When sample sizes are equal (Ji = J). the...Ch. 10.3 - Reconsider Example 10.8 involving an investigation...Ch. 10.3 - When sample sizes are not equal, the non...Ch. 10.3 - In an experiment to compare the quality of four...Ch. 10.3 - Prob. 33E Ch. 10.3 - Simplify E(MSTr) for the random effects model when...Ch. 10 - An experiment was carried out to compare flow...Ch. 10 - Cortisol is a hormone that plays an important role...Ch. 10 - Numerous factors contribute to the smooth running...Ch. 10 - An article in the British scientific journal...Ch. 10 - Prob. 39SE Ch. 10 - Prob. 40SE Ch. 10 - Prob. 41SE Ch. 10 - The critical flicker frequency (cff) is the...Ch. 10 - Prob. 43SE Ch. 10 - Four types of mortarsordinary cement mortar (OCM)....Ch. 10 - Prob. 45SE Ch. 10 - Prob. 46SE

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