Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 13.2, Problem 11E
a.
To determine
Check whether there is any difference in compressive strength due to the rodding level.
b.
To determine
Find the P-value for F-statistics in part (a).
c.
To determine
Analyze the residuals from the experiment. Explain the conclusions drawn about the underlying model
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6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows:
P(X=-x) = P(X = x)=p. P(X=0)= 1-2p.
Show that there is equality in Chebyshev's inequality for X.
This means that Chebyshev's inequality, in spite of being rather crude, cannot be
improved without additional assumptions.
4. Prove that, for any random variable X, the minimum of EIX-al is attained for
a = med (X).
8. Recall, from Sect. 2.16.4, the likelihood ratio statistic, Ln, which was defined
as a product of independent, identically distributed random variables with mean
1 (under the so-called null hypothesis), and the, sometimes more convenient,
log-likelihood, log L, which was a sum of independent, identically distributed
random variables, which, however, do not have mean log 1 = 0.
(a) Verify that the last claim is correct, by proving the more general statement,
namely that, if Y is a non-negative random variable with finite mean, then
E(log Y) log(EY).
(b) Prove that, in fact, there is strict inequality:
E(log Y) < log(EY),
unless Y is degenerate.
(c) Review the proof of Jensen's inequality, Theorem 5.1. Generalize with a
glimpse on (b).
Chapter 13 Solutions
Applied Statistics and Probability for Engineers
Ch. 13.2 - 13-1. Consider the following computer output.
(a)...Ch. 13.2 - 13-2. Consider the following computer output for...Ch. 13.2 - Prob. 3ECh. 13.2 - 13-4. An article in Nature describes an experiment...Ch. 13.2 - 13-5. In Design and Analysis of Experiments, 8th...Ch. 13.2 - 13-6. In “Orthogonal Design for Process...Ch. 13.2 - 13-7. The compressive strength of concrete is...Ch. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - 13-10. An article in Environment International...
Ch. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - 13-17 An experiment was run to determine whether...Ch. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - For each of the following exercises, use the...Ch. 13.2 - Prob. 25ECh. 13.2 - Prob. 26ECh. 13.2 - Prob. 27ECh. 13.2 - Prob. 28ECh. 13.2 - Prob. 29ECh. 13.2 - 13-30. Suppose that four normal populations have...Ch. 13.2 - Prob. 31ECh. 13.2 - Prob. 32ECh. 13.2 - Prob. 33ECh. 13.3 - 13-34. An article in the Journal of the...Ch. 13.3 - Prob. 35ECh. 13.3 - Prob. 36ECh. 13.3 - 13-37. An article in the Journal of Quality...Ch. 13.3 - 13-38. Consider the vapor-deposition experiment...Ch. 13.3 - Prob. 39ECh. 13.3 - 13-40. Reconsider Exercise 13-8 in which the...Ch. 13.3 - Prob. 41ECh. 13.4 - 13-42. Consider the following computer output from...Ch. 13.4 - 13-43. Consider the following computer output from...Ch. 13.4 - Prob. 44ECh. 13.4 - 13-45. Reconsider the experiment of Exercise 13-5....Ch. 13.4 - 13-46. An article in Quality Engineering...Ch. 13.4 - 13-47. In “The Effect of Nozzle Design on the...Ch. 13.4 - 13-48. In Design and Analysis of Experiments, 8th...Ch. 13.4 - Prob. 49ECh. 13.4 - 13-50. An article in the Food Technology Journal...Ch. 13.4 - 13-51. An experiment was conducted to investigate...Ch. 13 - Prob. 52SECh. 13 - 13-53. Consider the following computer...Ch. 13 - 13-54. An article in Lubrication Engineering...Ch. 13 - 13-55. An article in the IEEE Transactions on...Ch. 13 - Prob. 56SECh. 13 - Prob. 57SECh. 13 - Prob. 58SECh. 13 - Prob. 59SECh. 13 - Prob. 60SECh. 13 - Prob. 61SECh. 13 - Prob. 62SECh. 13 - Prob. 63SECh. 13 - Prob. 64SECh. 13 - Prob. 65SECh. 13 - Prob. 66SECh. 13 - Prob. 67SECh. 13 - 13-68. Consider testing the equality of the means...Ch. 13 - Prob. 69SECh. 13 - Prob. 70SECh. 13 - 13-72. Consider the single-factor completely...Ch. 13 - 13-73. Consider the single-factor completely...Ch. 13 - Prob. 74SECh. 13 - Prob. 75SECh. 13 - Prob. 76SECh. 13 - Prob. 77SE
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