STATS:DATA+MODELS-W/DVD
4th Edition
ISBN: 9780321986498
Author: DeVeaux
Publisher: PEARSON
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Question
Chapter 21, Problem 30E
a.
To determine
Explain the power of test.
b.
To determine
Explain the way to increase the power.
c.
To determine
Explain the disadvantage of lowering the cut off score.
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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 21 Solutions
STATS:DATA+MODELS-W/DVD
Ch. 21.4 - Prob. 1JCCh. 21.4 - Prob. 2JCCh. 21.4 - Prob. 3JCCh. 21.5 - Prob. 4JCCh. 21.5 - Prob. 5JCCh. 21.5 - Prob. 6JCCh. 21 - Prob. 3ECh. 21 - 4. More P-values Which of the following are true?...Ch. 21 - Prob. 7ECh. 21 - 6. Alpha false and true Which of the following...
Ch. 21 - Prob. 9ECh. 21 - Prob. 10ECh. 21 - Prob. 19ECh. 21 - 10. Significant again? A new reading program may...Ch. 21 - Prob. 11ECh. 21 - Prob. 12ECh. 21 - Prob. 15ECh. 21 - 14. Another P-value Have harsher penalties and ad...Ch. 21 - Prob. 17ECh. 21 - 16. Alpha, again Environmentalists concerned about...Ch. 21 - Prob. 21ECh. 21 - Prob. 22ECh. 21 - Approval 2014 In March 2014, Barack Obama’s...Ch. 21 - Prob. 24ECh. 21 - Prob. 25ECh. 21 - Prob. 26ECh. 21 - Prob. 27ECh. 21 - Prob. 28ECh. 21 - Prob. 29ECh. 21 - Prob. 30ECh. 21 - Prob. 31ECh. 21 - 28. Alzheimer’s Testing for Alzheimer’s disease...Ch. 21 - Prob. 33ECh. 21 - 30. Quality control Production managers on an...Ch. 21 - Prob. 35ECh. 21 - Prob. 36ECh. 21 - Prob. 37ECh. 21 - 34. Stop signs Highway safety engineers test new...Ch. 21 - Prob. 39ECh. 21 - 36. Ads A company is willing to renew its...Ch. 21 - Prob. 41ECh. 21 - Prob. 42ECh. 21 - Prob. 43ECh. 21 - 40. Catheters During an angiogram, heart problems...Ch. 21 - Prob. 45ECh. 21 - 42. Catheters, again The catheter company in...Ch. 21 - Prob. 47ECh. 21 - Prob. 48ECh. 21 - Prob. 49ECh. 21 - Prob. 50ECh. 21 - Prob. 1ECh. 21 - Prob. 2ECh. 21 - Prob. 5ECh. 21 - Prob. 6ECh. 21 - Prob. 13ECh. 21 - Prob. 14E
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