Statistics: Informed Decisions Using Data (5th Edition)
5th Edition
ISBN: 9780134133539
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 1.5, Problem 34AYU
To determine
To research: The polling done by Gallup in the 1936 and 1948 elections.
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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 1 Solutions
Statistics: Informed Decisions Using Data (5th Edition)
Ch. 1.1 - Vocabulary and Skill Building
1. Define...Ch. 1.1 - Vocabulary and Skill Building
2. Explain the...Ch. 1.1 - Vocabulary and Skill Building
3. A(n) ______ is a...Ch. 1.1 - Vocabulary and Skill Building
4. ______ statistics...Ch. 1.1 - Vocabulary and Skill Building
5. A(n) ______ is a...Ch. 1.1 - Vocabulary and Skill Building
6. ______ are the...Ch. 1.1 - Vocabulary and Skill Building
In Problems 7–14,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 7–14,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 7–14,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 7–14,...
Ch. 1.1 - Vocabulary and Skill Building
In Problems 7–14,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 7–14,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 7–14,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 7–14,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 15–22,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 15–22,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 15–22,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 15–22,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 15–22,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 15–22,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 15–22,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 15–22,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 23–30,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 23–30,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 23–30,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 23–30,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 23–30,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 23–30,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 23–30,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 23–30,...Ch. 1.1 - Prob. 31AYUCh. 1.1 - Vocabulary and Skill Building
In Problems 31–38,...Ch. 1.1 - Prob. 33AYUCh. 1.1 - Prob. 34AYUCh. 1.1 - Vocabulary and Skill Building
In Problems 31–38,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 31–38,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 31–38,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 31–38,...Ch. 1.1 - Vocabulary and Skill Building
In Problems 39–44, a...Ch. 1.1 - Vocabulary and Skill Building
In Problems 39–44, a...Ch. 1.1 - Vocabulary and Skill Building
In Problems 39–44, a...Ch. 1.1 - Vocabulary and Skill Building
In Problems 39–44, a...Ch. 1.1 - Vocabulary and Skill Building
In Problems 39–44, a...Ch. 1.1 - Vocabulary and Skill Building
In Problems 39–44, a...Ch. 1.1 - Vocabulary and Skill Building
In Problems 45 and...Ch. 1.1 - Vocabulary and Skill Building
In Problems 45 and...Ch. 1.1 - Vocabulary and Skill Building
Applying the...Ch. 1.1 - Vocabulary and Skill Building
Applying the...Ch. 1.1 - Vocabulary and Skill Building
Applying the...Ch. 1.1 - Vocabulary and Skill Building
Applying the...Ch. 1.1 - Vocabulary and Skill Building
Applying the...Ch. 1.1 - Vocabulary and Skill Building
Applying the...Ch. 1.1 - Vocabulary and Skill Building
Applying the...Ch. 1.1 - Vocabulary and Skill Building
Explaining the...Ch. 1.1 - Prob. 55AYUCh. 1.1 - Prob. 56AYUCh. 1.1 - Vocabulary and Skill Building
Explaining the...Ch. 1.1 - Vocabulary and Skill Building
Explaining the...Ch. 1.1 - Prob. 59AYUCh. 1.2 - Vocabulary and Skill Building
1. In your own...Ch. 1.2 - Vocabulary and Skill Building
2. What is an...Ch. 1.2 - Prob. 3AYUCh. 1.2 - Vocabulary and Skill Building
4. Given a choice,...Ch. 1.2 - Prob. 5AYUCh. 1.2 - Vocabulary and Skill Building
6. The data used in...Ch. 1.2 - Prob. 7AYUCh. 1.2 - Vocabulary and Skill Building
8. What does it mean...Ch. 1.2 - Prob. 9AYUCh. 1.2 - Vocabulary and Skill Building
In Problems 9–16,...Ch. 1.2 - Prob. 11AYUCh. 1.2 - Vocabulary and Skill Building
In Problems 9–16,...Ch. 1.2 - Vocabulary and Skill Building
In Problems 9–16,...Ch. 1.2 - Vocabulary and Skill Building
In Problems 9–16,...Ch. 1.2 - Prob. 15AYUCh. 1.2 - Vocabulary and Skill Building
In Problems 9–16,...Ch. 1.2 - Prob. 17AYUCh. 1.2 - Prob. 18AYUCh. 1.2 - Prob. 19AYUCh. 1.2 - Prob. 20AYUCh. 1.2 - Vocabulary and Skill Building
Applying the...Ch. 1.2 - Prob. 22AYUCh. 1.2 - Prob. 23AYUCh. 1.2 - Vocabulary and Skill Building
Applying the...Ch. 1.3 - Vocabulary and Skill Building
1. What is a frame?
Ch. 1.3 - Vocabulary and Skill Building
2. Define simple...Ch. 1.3 - Vocabulary and Skill Building
3. What does it mean...Ch. 1.3 - Vocabulary and Skill Building
4. What is random...Ch. 1.3 - Vocabulary and Skill Building
5. Literature As...Ch. 1.3 - Vocabulary and Skill Building
6. Team Captains A...Ch. 1.3 - Vocabulary and Skill Building
NW 7. Course...Ch. 1.3 - Vocabulary and Skill Building
8. Merit Badge...Ch. 1.3 - Vocabulary and Skill Building
Applying the...Ch. 1.3 - Vocabulary and Skill Building
Applying the...Ch. 1.3 - Vocabulary and Skill Building
Applying the...Ch. 1.3 - Vocabulary and Skill Building
Applying the...Ch. 1.3 - Vocabulary and Skill Building
Applying the...Ch. 1.3 - Vocabulary and Skill Building
Applying the...Ch. 1.3 - Vocabulary and Skill Building
Applying the...Ch. 1.3 - Prob. 16AYUCh. 1.4 - Vocabulary and Skill Building
1. Describe a...Ch. 1.4 - Vocabulary and Skill Building
2. Which sampling...Ch. 1.4 - Vocabulary and Skill Building
3. Why are...Ch. 1.4 - Vocabulary and Skill Building
4. A(n) ______...Ch. 1.4 - Vocabulary and Skill Building
5. A(n) ______...Ch. 1.4 - Vocabulary and Skill Building
6. True or False:...Ch. 1.4 - Vocabulary and Skill Building
7. True or False: A...Ch. 1.4 - Vocabulary and Skill Building
8. True or False:...Ch. 1.4 - Vocabulary and Skill Building
9. True or False:...Ch. 1.4 - Vocabulary and Skill Building
10. True or False:...Ch. 1.4 - Vocabulary and Skill Building
In Problems 11–22,...Ch. 1.4 - Vocabulary and Skill Building
In Problems 11–22,...Ch. 1.4 - Vocabulary and Skill Building
In Problems 11–22,...Ch. 1.4 - Vocabulary and Skill Building
In Problems 11–22,...Ch. 1.4 - Vocabulary and Skill Building
In Problems 11–22,...Ch. 1.4 - Prob. 16AYUCh. 1.4 - Prob. 17AYUCh. 1.4 - Prob. 18AYUCh. 1.4 - Prob. 19AYUCh. 1.4 - Prob. 20AYUCh. 1.4 - Vocabulary and Skill Building
In Problems 11–22,...Ch. 1.4 - Prob. 22AYUCh. 1.4 - Prob. 23AYUCh. 1.4 - Vocabulary and Skill Building
24. A...Ch. 1.4 - Vocabulary and Skill Building
Applying the...Ch. 1.4 - Prob. 26AYUCh. 1.4 - Prob. 27AYUCh. 1.4 - Prob. 28AYUCh. 1.4 - Vocabulary and Skill Building
Applying the...Ch. 1.4 - Prob. 30AYUCh. 1.4 - Prob. 31AYUCh. 1.4 - Prob. 32AYUCh. 1.4 - Prob. 33AYUCh. 1.4 - Prob. 34AYUCh. 1.4 - Prob. 35AYUCh. 1.4 - Prob. 36AYUCh. 1.4 - Vocabulary and Skill Building
Applying the...Ch. 1.4 - Prob. 38AYUCh. 1.4 - Vocabulary and Skill Building
Applying the...Ch. 1.4 - Prob. 40AYUCh. 1.5 - Vocabulary and Skill Building
1. What is a closed...Ch. 1.5 - Vocabulary and Skill Building
2. What does it mean...Ch. 1.5 - Vocabulary and Skill Building
3. What is bias?...Ch. 1.5 - Vocabulary and Skill Building
4. Distinguish...Ch. 1.5 - Vocabulary and Skill Building
5. A retail store...Ch. 1.5 - Prob. 6AYUCh. 1.5 - Vocabulary and Skill Building
7. An antigun...Ch. 1.5 - Vocabulary and Skill Building
8. Suppose you are...Ch. 1.5 - Prob. 9AYUCh. 1.5 - Vocabulary and Skill Building
10. Cold Stone...Ch. 1.5 - Prob. 11AYUCh. 1.5 - Prob. 12AYUCh. 1.5 - Prob. 13AYUCh. 1.5 - Prob. 14AYUCh. 1.5 - Vocabulary and Skill Building
15. Suppose you are...Ch. 1.5 - Vocabulary and Skill Building
16. To determine the...Ch. 1.5 - Prob. 17AYUCh. 1.5 - Prob. 18AYUCh. 1.5 - Prob. 19AYUCh. 1.5 - 20. Order of the Questions Consider the following...Ch. 1.5 - Prob. 21AYUCh. 1.5 - Prob. 22AYUCh. 1.5 - Prob. 23AYUCh. 1.5 - Prob. 24AYUCh. 1.5 - Prob. 25AYUCh. 1.5 - 26. Current Population Survey In the federal...Ch. 1.5 - Prob. 27AYUCh. 1.5 - 28. Write Your Own Survey Develop a survey that...Ch. 1.5 - Prob. 29AYUCh. 1.5 - 30. Wording Survey Questions Write a survey...Ch. 1.5 - Prob. 31AYUCh. 1.5 - Prob. 32AYUCh. 1.5 - Prob. 33AYUCh. 1.5 - Prob. 34AYUCh. 1.5 - Prob. 35AYUCh. 1.5 - Prob. 36AYUCh. 1.5 - Prob. 37AYUCh. 1.5 - Prob. 38AYUCh. 1.5 - Prob. 39AYUCh. 1.5 - Prob. 40AYUCh. 1.5 - Prob. 41AYUCh. 1.5 - Prob. 42AYUCh. 1.5 - 43. Suppose a survey asks, "Do you own any CDs?"...Ch. 1.5 - 44. Discuss a possible advantage of offering...Ch. 1.6 - 1. Define the following:
(a) Experimental unit
(b)...Ch. 1.6 - 2. What is replication in an experiment?
Ch. 1.6 - 3. Explain the difference between a single-blind...Ch. 1.6 - 4. A(n) ______ ______ design is one in which each...Ch. 1.6 - 5. Grouping together similar experimental units...Ch. 1.6 - Prob. 6AYUCh. 1.6 - Prob. 7AYUCh. 1.6 - 8. Alcohol Dependence To determine if topiramate...Ch. 1.6 - 9. School Psychology A school psychologist wants...Ch. 1.6 - Prob. 10AYUCh. 1.6 - Prob. 11AYUCh. 1.6 - 12. Assessment To help assess student learning in...Ch. 1.6 - Prob. 13AYUCh. 1.6 - Prob. 14AYUCh. 1.6 - Prob. 15AYUCh. 1.6 - Prob. 16AYUCh. 1.6 - 17. Dominant Hand Professor Andy Neill wanted to...Ch. 1.6 - Prob. 18AYUCh. 1.6 - Prob. 19AYUCh. 1.6 - Prob. 20AYUCh. 1.6 - 21. Drug Effectiveness A pharmaceutical company...Ch. 1.6 - 22. Effects of Alcohol A researcher has recruited...Ch. 1.6 - 23. Green Tea You wonder whether green tea lowers...Ch. 1.6 - Prob. 24AYUCh. 1.6 - Prob. 25AYUCh. 1.6 - Prob. 26AYUCh. 1.6 - Prob. 27AYUCh. 1.6 - Prob. 28AYUCh. 1.6 - Prob. 29AYUCh. 1.6 - Prob. 30AYUCh. 1.6 - Prob. 31AYUCh. 1.6 - Prob. 32AYUCh. 1.6 - Prob. 33AYUCh. 1.6 - Prob. 34AYUCh. 1.6 - Prob. 35AYUCh. 1.6 - Prob. 36AYUCh. 1 - Prob. 1RECh. 1 - In Problems 1–5, provide a definition using your...Ch. 1 - In Problems 1–5, provide a definition using your...Ch. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - 6. List and describe the three major types of...Ch. 1 - Prob. 7RECh. 1 - 8. List and explain the three sources of bias in...Ch. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - In Problems 14 and 15, determine whether the...Ch. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - In Problems 20 and 21, determine whether the study...Ch. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - In Problems 23–26, determine the type of sampling...Ch. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - 1. List the four components that comprise the...Ch. 1 - Prob. 2CTCh. 1 - Prob. 3CTCh. 1 - Prob. 4CTCh. 1 - In Problems 3–5, determine if the variable is...Ch. 1 - Prob. 6CTCh. 1 - Prob. 7CTCh. 1 - Prob. 8CTCh. 1 - Prob. 9CTCh. 1 - Prob. 10CTCh. 1 - Prob. 11CTCh. 1 - 12. A cellular phone company is looking for ways...Ch. 1 - Prob. 13CTCh. 1 - Prob. 14CTCh. 1 - Prob. 15CTCh. 1 - Prob. 16CTCh. 1 - Prob. 17CTCh. 1 - Prob. 18CTCh. 1 - Prob. 19CTCh. 1 - Prob. 20CTCh. 1 - Prob. 21CTCh. 1 - Prob. 1CSCh. 1 - Prob. 2CSCh. 1 - Prob. 3CSCh. 1 - Prob. 4CS
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