Essentials of Statistics (6th Edition)
6th Edition
ISBN: 9780134687155
Author: Triola
Publisher: PEARSON
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Chapter 7.3, Problem 4BSC
Normality Requirement What is different about the normality requirement for a confidence
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Throughout, A, B, (An, n≥ 1), and (Bn, n≥ 1) are subsets of 2.
1. Show that
AAB (ANB) U (BA) = (AUB) (AB),
Α' Δ Β = Α Δ Β,
{A₁ U A2} A {B₁ U B2) C (A1 A B₁}U{A2 A B2).
16. Show that, if X and Y are independent random variables, such that E|X|< ∞,
and B is an arbitrary Borel set, then
EXI{Y B} = EX P(YE B).
Proposition 1.1 Suppose that X1, X2,... are random variables. The following
quantities are random variables:
(a) max{X1, X2) and min(X1, X2);
(b) sup, Xn and inf, Xn;
(c) lim sup∞ X
and lim inf∞ Xn-
(d) If Xn(w) converges for (almost) every w as n→ ∞, then lim-
random variable.
→ Xn is a
Chapter 7 Solutions
Essentials of Statistics (6th Edition)
Ch. 7.1 - Poll Results in the Media USA Today provided...Ch. 7.1 - Margin of Error For the poll described in Exercise...Ch. 7.1 - Notation For the poll described in Exercise 1,...Ch. 7.1 - Confidence Levels Given specific sample data, such...Ch. 7.1 - Finding Critical Values. In Exercises 58, find the...Ch. 7.1 - Finding Critical Values. In Exercises 58, find the...Ch. 7.1 - Finding Critical Values. In Exercises 58, find the...Ch. 7.1 - Finding Critical Values. In Exercises 58, find the...Ch. 7.1 - Formats of Confidence Intervals. In Exercises 912,...Ch. 7.1 - Formats of Confidence Intervals. In Exercises 912,...
Ch. 7.1 - Formats of Confidence Intervals. In Exercises 912,...Ch. 7.1 - Formats of Confidence Intervals. In Exercises 912,...Ch. 7.1 - Constructing and Interpreting Confidence...Ch. 7.1 - Constructing and Interpreting Confidence...Ch. 7.1 - Constructing and Interpreting Confidence...Ch. 7.1 - Constructing and Interpreting Confidence...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Touch Therapy When she was 9 years of age, Emily...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Critical Thinking. In Exercises 1728, use the data...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Determining Sample Size. In Exercises 3138, use...Ch. 7.1 - Finite Population Correction Factor For Formulas...Ch. 7.1 - One-Sided Confidence Interval A one-sided claim...Ch. 7.1 - Coping with No Success According to the Rule of...Ch. 7.2 - In Exercises 13, refer to the accompanying screen...Ch. 7.2 - Statistical Literacy and Critical Thinking In...Ch. 7.2 - In Exercises 13, refer to the accompanying screen...Ch. 7.2 - Normality Requirement What does it mean when we...Ch. 7.2 - Using Correct Distribution. In Exercises 58,...Ch. 7.2 - Using Correct Distribution. In Exercises 58,...Ch. 7.2 - Using Correct Distribution. In Exercises 58,...Ch. 7.2 - Using Correct Distribution. In Exercises 58,...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Confidence Intervals. In Exercises 924, construct...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Sample Size. In Exercises 2936, find the sample...Ch. 7.2 - Confidence Interval with Known . In Exercises 37...Ch. 7.2 - Confidence Interval with Known . In Exercises 37...Ch. 7.2 - Finite Population Correction Factor If a simple...Ch. 7.3 - Brain Volume Using all of the brain volumes listed...Ch. 7.3 - Expressing Confidence Intervals Example 2 showed...Ch. 7.3 - Last Digit Analysis The dotplot below depicts the...Ch. 7.3 - Normality Requirement What is different about the...Ch. 7.3 - Finding Critical Values and Confidence Intervals....Ch. 7.3 - Finding Critical Values and Confidence Intervals....Ch. 7.3 - Finding Critical Values and Confidence Intervals....Ch. 7.3 - Finding Critical Values and Confidence Intervals....Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Finding Confidence Intervals. In Exercises 916,...Ch. 7.3 - Comparing Waiting Lines a. The values listed below...Ch. 7.3 - Determining Sample Size. In Exercises 1922, assume...Ch. 7.3 - Determining Sample Size. In Exercises 1922, assume...Ch. 7.3 - Determining Sample Size. In Exercises 1922, assume...Ch. 7.3 - Determining Sample Size. In Exercises 1922, assume...Ch. 7.3 - Finding Critical Values In constructing confidence...Ch. 7.3 - Finding Sample Size Instead of using Table 7-2 for...Ch. 7.4 - Replacement Why does the bootstrap method require...Ch. 7.4 - Bootstrap Sample Here is a random sample of...Ch. 7.4 - Bootstrap Sample Given the sample data from...Ch. 7.4 - Prob. 4BSCCh. 7.4 - In Exercises 58, use the relatively small number...Ch. 7.4 - In Exercises 58, use the relatively small number...Ch. 7.4 - In Exercises 58, use the relatively small number...Ch. 7.4 - In Exercises 58, use the relatively small number...Ch. 7 - Celebrities and the Law Here is a 95% confidence...Ch. 7 - Interpreting CI Write a brief statement that...Ch. 7 - Critical Value For the survey described in...Ch. 7 - Loose Change USA Today reported that 40% of people...Ch. 7 - Sample Size for Proportion Find the sample size...Ch. 7 - Sample Size for Mean Find the sample size required...Ch. 7 - Requirements A quality control analyst has...Ch. 7 - Degrees of Freedom In general, what does degrees...Ch. 7 - Critical Value Refer to Exercise 7 Requirements...Ch. 7 - Which Method? Refer to Exercise 7 Requirements and...Ch. 7 - Online News In a Harris poll of 2036 adults, 40%...Ch. 7 - Computers In order to better plan for student...Ch. 7 - Earthquake Magnitudes Listed below are Richter...Ch. 7 - Lefties There have been several studies conducted...Ch. 7 - Distributions Identify the distribution (normal,...Ch. 7 - Sample Size You have been hired by your new...Ch. 7 - Wristwatch Accuracy Students of the author...Ch. 7 - Wristwatch Accuracy Use the sample data from...Ch. 7 - Flight Arrivals. Listed below are the arrival...Ch. 7 - Flight Arrivals. Listed below are the arrival...Ch. 7 - Flight Arrivals. Listed below are the arrival...Ch. 7 - Flight Arrivals. Listed below are the arrival...Ch. 7 - Normal Distribution Using a larger data set than...Ch. 7 - Sample Size Find the sample size necessary to...Ch. 7 - Prob. 7CRECh. 7 - Normality Assessment A random sample consists of...Ch. 7 - Critical Thinking: What does the survey tell us?...Ch. 7 - Critical Thinking: What does the survey tell us?...Ch. 7 - Critical Thinking: What does the survey tell us?...Ch. 7 - Critical Thinking: What does the survey tell us?...Ch. 7 - Critical Thinking: What does the survey tell us?...
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- Exercise 4.2 Prove that, if A and B are independent, then so are A and B, Ac and B, and A and B.arrow_forward8. Show that, if {Xn, n ≥ 1) are independent random variables, then sup X A) < ∞ for some A.arrow_forward8- 6. Show that, for any random variable, X, and a > 0, 8 心 P(xarrow_forward15. This problem extends Problem 20.6. Let X, Y be random variables with finite mean. Show that 00 (P(X ≤ x ≤ Y) - P(X ≤ x ≤ X))dx = E Y — E X.arrow_forward(b) Define a simple random variable. Provide an example.arrow_forward17. (a) Define the distribution of a random variable X. (b) Define the distribution function of a random variable X. (c) State the properties of a distribution function. (d) Explain the difference between the distribution and the distribution function of X.arrow_forward16. (a) Show that IA(w) is a random variable if and only if A E Farrow_forward15. Let 2 {1, 2,..., 6} and Fo({1, 2, 3, 4), (3, 4, 5, 6}). (a) Is the function X (w) = 21(3, 4) (w)+711.2,5,6) (w) a random variable? Explain. (b) Provide a function from 2 to R that is not a random variable with respect to (N, F). (c) Write the distribution of X. (d) Write and plot the distribution function of X.arrow_forward20. Define the o-field R2. Explain its relation to the o-field R.arrow_forward7. Show that An → A as n→∞ I{An} - → I{A} as n→ ∞.arrow_forward7. (a) Show that if A,, is an increasing sequence of measurable sets with limit A = Un An, then P(A) is an increasing sequence converging to P(A). (b) Repeat the same for a decreasing sequence. (c) Show that the following inequalities hold: P (lim inf An) lim inf P(A) ≤ lim sup P(A) ≤ P(lim sup A). (d) Using the above inequalities, show that if A, A, then P(A) + P(A).arrow_forward19. (a) Define the joint distribution and joint distribution function of a bivariate ran- dom variable. (b) Define its marginal distributions and marginal distribution functions. (c) Explain how to compute the marginal distribution functions from the joint distribution function.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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