Statistics
13th Edition
ISBN: 9780135820100
Author: MCCLAVE, James T., Sincich, Terry
Publisher: PEARSON
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Chapter 12.9, Problem 118UP
To determine
Explain the reason why the F-test used to compare complete and reduced models is a one-tailed, upper-tailed test.
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9. The concentration function of a random variable X is defined as
Qx(h) = sup P(x ≤ X ≤x+h), h>0.
x
(a) Show that Qx+b (h) = Qx(h).
(b) Is it true that Qx(ah) =aQx(h)?
(c) Show that, if X and Y are independent random variables, then
Qx+y (h) min{Qx(h). Qy (h)).
To put the concept in perspective, if X1, X2, X, are independent, identically
distributed random variables, and S₁ = Z=1Xk, then there exists an absolute
constant, A, such that
A
Qs, (h) ≤
√n
Some references: [79, 80, 162, 222], and [204], Sect. 1.5.
29
Suppose that a mound-shaped data set has a
must mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 6 and 12?
b. About what percentage of the data should
lie between 4 and 6?
c. About what percentage of the data should
lie below 4?
91002 175/1
3
2,3,
ample
and
rical
t?
the
28 Suppose that a mound-shaped data set has a
mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 8 and 12?
b. About what percentage of the data should
lie above 10?
c. About what percentage of the data should
lie above 12?
Chapter 12 Solutions
Statistics
Ch. 12.3 - 12.1 Write a first-order model relating E(y)...Ch. 12.3 - Prob. 2UPCh. 12.3 - Outline the six steps in a multiple-regression...Ch. 12.3 - Prob. 4UPCh. 12.3 - Prob. 5UPCh. 12.3 - MINITAB was used to fit the model y = β0 + β1x1 +...Ch. 12.3 - Prob. 7LMCh. 12.3 - Prob. 8LMCh. 12.3 - Prob. 9LMCh. 12.3 - Prob. 10LM
Ch. 12.3 - Prob. 11LMCh. 12.3 - 12.8 If the analysis of variance F-test leads to...Ch. 12.3 - Prob. 13ACBCh. 12.3 - Prob. 14ACBCh. 12.3 - Prob. 15ACBCh. 12.3 - Dating and disclosure. Refer to the Journal of...Ch. 12.3 - Prob. 17ACBCh. 12.3 - Prob. 18ACBCh. 12.3 - Prob. 20ACBCh. 12.3 - Study of adolescents with ADHD. Children with...Ch. 12.3 - Prob. 22ACICh. 12.3 - Prob. 23ACICh. 12.3 - A rubber additive made from cashew nut shells....Ch. 12.3 - Prob. 25ACICh. 12.3 - Prob. 26ACICh. 12.3 - Cooling method for gas turbines. Refer to the...Ch. 12.3 - Prob. 28ACICh. 12.3 - Prob. 29ACICh. 12.3 - Prob. 30ACACh. 12.4 - Prob. 31UPCh. 12.4 - Prob. 32UPCh. 12.4 - Prob. 33ACBCh. 12.4 - Prob. 35ACBCh. 12.4 - Prob. 36ACBCh. 12.4 - Prob. 37ACBCh. 12.4 - Prob. 38ACICh. 12.4 - Prob. 39ACICh. 12.4 - Prob. 40ACICh. 12.4 - Prob. 41ACICh. 12.5 - Prob. 42UPCh. 12.5 - Prob. 43UPCh. 12.5 - Prob. 44LMCh. 12.5 - Prob. 45LMCh. 12.5 - MINITAB was used to fit the model
y = β0 + β1x1 +...Ch. 12.5 - Prob. 47ACBCh. 12.5 - Prob. 48ACBCh. 12.5 - Prob. 49ACBCh. 12.5 - Prob. 51ACBCh. 12.5 - Prob. 52ACBCh. 12.5 - Prob. 53ACICh. 12.5 - Prob. 54ACICh. 12.5 - Prob. 55ACICh. 12.5 - Prob. 56ACICh. 12.5 - Prob. 57ACICh. 12.5 - Prob. 58ACICh. 12.5 - Prob. 59ACICh. 12.6 - Prob. 60UPCh. 12.6 - 12.49 Write a second-order model relating the mean...Ch. 12.6 - Prob. 62LMCh. 12.6 - Prob. 63LMCh. 12.6 - Prob. 64LMCh. 12.6 - Prob. 65LMCh. 12.6 - Prob. 66ACBCh. 12.6 - Prob. 67ACBCh. 12.6 - Childhood obesity study. The eating patterns of...Ch. 12.6 - Prob. 69ACBCh. 12.6 - Prob. 70ACBCh. 12.6 - Prob. 71ACBCh. 12.6 - Prob. 72ACBCh. 12.6 - Prob. 73ACBCh. 12.6 - Prob. 74ACICh. 12.6 - Prob. 75ACICh. 12.6 - Prob. 76ACICh. 12.6 - Prob. 77ACICh. 12.6 - Prob. 78ACICh. 12.6 - Prob. 79ACICh. 12.6 - Prob. 80ACACh. 12.7 - Prob. 81UPCh. 12.7 - Prob. 82UPCh. 12.7 - Prob. 83LMCh. 12.7 -
MINITAB was used to fit the model
y = β0 + β1x1 +...Ch. 12.7 - Prob. 85ACBCh. 12.7 - Prob. 86ACBCh. 12.7 - Prob. 87ACBCh. 12.7 - Prob. 88ACBCh. 12.7 - Prob. 89ACBCh. 12.7 - Prob. 90ACBCh. 12.7 - Prob. 91ACBCh. 12.7 - Prob. 92ACICh. 12.7 - Prob. 93ACICh. 12.7 - Prob. 94ACICh. 12.7 - Prob. 96ACICh. 12.7 - Prob. 97ACICh. 12.7 - Prob. 98ACICh. 12.7 - Prob. 99ACACh. 12.8 - 12.82 Consider a multiple regression model for a...Ch. 12.8 - Prob. 101UPCh. 12.8 - Prob. 102UPCh. 12.8 - Prob. 103LMCh. 12.8 - Prob. 104LMCh. 12.8 - Reality TV and cosmetic surgery. Refer to the Body...Ch. 12.8 - Prob. 106ACBCh. 12.8 - Prob. 108ACBCh. 12.8 - Prob. 110ACBCh. 12.8 - Prob. 111ACICh. 12.8 - Prob. 112ACICh. 12.8 - 12.91 Workplace bullying and intention to leave....Ch. 12.8 - Prob. 114ACICh. 12.8 - Prob. 116ACACh. 12.9 - Prob. 117UPCh. 12.9 - Prob. 118UPCh. 12.9 - Prob. 119UPCh. 12.9 - Prob. 120LMCh. 12.9 - Prob. 121LMCh. 12.9 - Prob. 122ACBCh. 12.9 - Prob. 123ACBCh. 12.9 - Mental health of a community. An article in the...Ch. 12.9 - Prob. 125ACBCh. 12.9 - Prob. 126ACBCh. 12.9 - Prob. 127ACBCh. 12.9 - Prob. 128ACICh. 12.9 - Prob. 129ACICh. 12.9 - Glass as a waste encapsulant. The encapsulation of...Ch. 12.9 - Whales entangled in fishing gear. Refer to the...Ch. 12.9 - Agreeableness, gender, and wages. Refer to the...Ch. 12.9 - Prob. 133ACICh. 12.9 - Prob. 134ACACh. 12.10 - Prob. 135UPCh. 12.10 - Prob. 136UPCh. 12.10 - Prob. 137LMCh. 12.10 - Prob. 138ACBCh. 12.10 - Prob. 139ACBCh. 12.10 - 12.114 Accuracy of software effort estimates....Ch. 12.10 - Prob. 141ACBCh. 12.10 - Prob. 142ACBCh. 12.10 - Prob. 143ACICh. 12.10 - Prob. 144ACICh. 12.10 - Prob. 145ACICh. 12.12 - Define a regression residual.
Ch. 12.12 - Prob. 147UPCh. 12.12 - Give two properties of the regression residuals...Ch. 12.12 - True or False. Regression models fit to...Ch. 12.12 - Define multicollinearity in regression.
Ch. 12.12 - Give three indicators of a multicollinearity...Ch. 12.12 - Define extrapolation.
Ch. 12.12 - 12.123 State casket sales restrictions. Some...Ch. 12.12 - Identify the problem(s) in each of the residual...Ch. 12.12 - Dating and disclosure. Refer to the Journal of...Ch. 12.12 - State casket sales restrictions. Some states...Ch. 12.12 - Personality traits and job performance. Refer to...Ch. 12.12 - Agreeableness, gender, and wages. Refer to the...Ch. 12.12 - Personality and aggressive behavior. Psychological...Ch. 12.12 - Yield strength of steel alloy. Refer to Exercise...Ch. 12.12 - Accuracy of software effort estimates. Refer to...Ch. 12.12 - Failure times of silicon wafer microchips. Refer...Ch. 12.12 - Arsenic in groundwater. Refer to the Environmental...Ch. 12.12 - A rubber additive made from cashew nut shells....Ch. 12.12 - Reality TV and cosmetic surgery. Refer to the Body...Ch. 12.12 - Cooling method for gas turbines. Refer to the...Ch. 12.12 - Emotional intelligence and team performance. Refer...Ch. 12.12 - Bubble behavior in subcooled flow boiling. Refer...Ch. 12 - Prob. 169UPCh. 12 - 12.141 Explain why stepwise regression is used....Ch. 12 - 12.140 It is desired to relate E(y) to a...Ch. 12 - 12.142 Consider relating E(y) to two quantitative...Ch. 12 - 12.136 Suppose you fit the model
to n = 25 data...Ch. 12 - 12.137 Suppose you used Minitab to fit the model
...Ch. 12 - 12.134 Suppose you have developed a regression...Ch. 12 - 12.138 The first-order model E (y) = β0 + β1x1 was...Ch. 12 - 12.143 To model the relationship between y, a...Ch. 12 - 12.144 Suppose you fit the regression model
to...Ch. 12 - Global warming and foreign investments. Scientists...Ch. 12 - Students’ ability in science. An article published...Ch. 12 - Glass as a waste encapsulant. The encapsulation of...Ch. 12 - Listen-and-look study. Where do you look when you...Ch. 12 - Defects in nuclear missile housing parts. The...Ch. 12 - Violent behavior in children. Refer to the...Ch. 12 - Improving SAT scores. Refer to the Chance (Winter...Ch. 12 - Factors identifying urban counties. The...Ch. 12 - Growth of Japanese beetles. In the Journal of...Ch. 12 - Prob. 188ACBCh. 12 - Snow geese feeding trial. Refer to the Journal of...Ch. 12 - Optimizing semiconductor material processing....Ch. 12 - 12.125 Women in top management. Refer to the...Ch. 12 - Comparing mosquito repellents. Which insect...Ch. 12 - Rating funny cartoons. Newspaper cartoons,...Ch. 12 - Prob. 194ACICh. 12 - Prob. 195ACICh. 12 - Prob. 196ACICh. 12 - Prob. 197ACICh. 12 - Prob. 198ACICh. 12 - 12.155 Entry-level job preferences. Benefits...Ch. 12 - Prob. 200ACICh. 12 - Prob. 201ACICh. 12 - Prob. 202ACICh. 12 - Prob. 205CTC
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- 27 Suppose that you have a data set of 1, 2, 2, 3, 3, 3, 4, 4, 5, and you assume that this sample represents a population. The mean is 3 and g the standard deviation is 1.225.10 a. Explain why you can apply the empirical rule to this data set. b. Where would "most of the values" in the population fall, based on this data set?arrow_forward30 Explain how you can use the empirical rule to find out whether a data set is mound- shaped, using only the values of the data themselves (no histogram available).arrow_forward5. Let X be a positive random variable with finite variance, and let A = (0, 1). Prove that P(X AEX) 2 (1-A)² (EX)² EX2arrow_forward
- 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.arrow_forward4. Prove that, for any random variable X, the minimum of EIX-al is attained for a = med (X).arrow_forward8. 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).arrow_forward
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