Essentials of Statistics (5th Edition)
5th Edition
ISBN: 9780321924599
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 7.2, Problem 4BSC
To determine
To identify: The wider confidence interval among 95% and 80% confidence levels.
To explain: Why the confidence interval is wider.
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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 (5th Edition)
Ch. 7.2 - 2. Margin of Error For the poll described in...Ch. 7.2 - Statistical Literacy and Critical Thinking
1. Poll...Ch. 7.2 - 3. Notation For the poll described in Exercise 1,...Ch. 7.2 - 4. Confidence Levels Given specific sample data,...Ch. 7.2 - Finding Critical Values. In Exercises 5-8, find...Ch. 7.2 - Prob. 6BSCCh. 7.2 - Finding Critical Values. In Exercises 5-8, find...Ch. 7.2 - Finding Critical Values. In Exercises 5-8, find...Ch. 7.2 - Formats of Confidence Intervals. In Exercises...Ch. 7.2 - Formats of Confidence Intervals. In Exercises...
Ch. 7.2 - Formats of Confidence Intervals. In Exercises...Ch. 7.2 - Formats of Confidence Intervals. In Exercises...Ch. 7.2 - Constructing and Interpreting Confidence...Ch. 7.2 - Constructing and Interpreting Confidence...Ch. 7.2 - Constructing and Interpreting Confidence...Ch. 7.2 - Constructing and Interpreting Confidence...Ch. 7.2 - 17. Gender Selection The Genetics and IVF...Ch. 7.2 - 18. Gender Selection The Genetics and IVF...Ch. 7.2 - Prob. 19BSCCh. 7.2 - 20. Mendelian Genetics When Mendel conducted his...Ch. 7.2 - 21. Online Books A Consumer Reports Research...Ch. 7.2 - 22. Want Boss’s Job? In a USA Today survey, 20.8%...Ch. 7.2 - 23. Job Interviews In a Harris poll of 514 human...Ch. 7.2 - 24. Job Interviews In a Harris poll of 514 human...Ch. 7.2 - Prob. 25BSCCh. 7.2 - Prob. 26BSCCh. 7.2 - Prob. 27BSCCh. 7.2 - Prob. 28BSCCh. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Prob. 33BSCCh. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Determining Sample Size. In Exercises 29-36, use...Ch. 7.2 - Using Appendix B Data Sets. In Exercises 37 and...Ch. 7.2 - Using Appendix B Data Sets. In Exercises 37 and...Ch. 7.2 - 39. Finite Population Correction Factor For...Ch. 7.2 - 40. Confidence Interval from Small Sample Special...Ch. 7.2 - Prob. 41BBCh. 7.2 - Prob. 42BBCh. 7.2 - Prob. 43BBCh. 7.3 - In Exercises 1-3, refer to the accompanying screen...Ch. 7.3 - Statistical Literacy and Critical Thinking
In...Ch. 7.3 - In Exercises 1-3, refer to the accompanying screen...Ch. 7.3 - 4. Normality Requirement What does it mean when we...Ch. 7.3 - Using Correct Distribution. In Exercises 5-8,...Ch. 7.3 - Using Correct Distribution. In Exercises 5-8,...Ch. 7.3 - Using Correct Distribution. In Exercises 5-8,...Ch. 7.3 - Using Correct Distribution. In Exercises 5-8,...Ch. 7.3 - Confidence Intervals. In Exercises 9-24, construct...Ch. 7.3 - Confidence Intervals. In Exercises 9-24, construct...Ch. 7.3 - Confidence Intervals. In Exercises 9-24, construct...Ch. 7.3 - Confidence Intervals. In Exercises 9-24, construct...Ch. 7.3 - Prob. 13BSCCh. 7.3 - Prob. 14BSCCh. 7.3 - Prob. 15BSCCh. 7.3 - Prob. 16BSCCh. 7.3 - Prob. 17BSCCh. 7.3 - Prob. 18BSCCh. 7.3 - Prob. 19BSCCh. 7.3 - Prob. 20BSCCh. 7.3 - Prob. 21BSCCh. 7.3 - Prob. 22BSCCh. 7.3 - Confidence Intervals. In Exercises 9-24, construct...Ch. 7.3 - Prob. 24BSCCh. 7.3 - Prob. 25BSCCh. 7.3 - Prob. 26BSCCh. 7.3 - Prob. 27BSCCh. 7.3 - Prob. 28BSCCh. 7.3 - Prob. 29BSCCh. 7.3 - Prob. 30BSCCh. 7.3 - Prob. 31BSCCh. 7.3 - Prob. 32BSCCh. 7.3 - Prob. 33BSCCh. 7.3 - Prob. 34BSCCh. 7.3 - Prob. 35BBCh. 7.3 - Prob. 36BBCh. 7.3 - Prob. 37BBCh. 7.3 - Prob. 38BBCh. 7.3 - Prob. 39BBCh. 7.3 - Prob. 40BBCh. 7.3 - Prob. 41BBCh. 7.4 - 1. LDL Cholesterol Using the 40 LDL cholesterol...Ch. 7.4 - Prob. 2BSCCh. 7.4 - Prob. 3BSCCh. 7.4 - Prob. 4BSCCh. 7.4 - Prob. 5BSCCh. 7.4 - Prob. 6BSCCh. 7.4 - Prob. 7BSCCh. 7.4 - Prob. 8BSCCh. 7.4 - Prob. 9BSCCh. 7.4 - Prob. 10BSCCh. 7.4 - Prob. 11BSCCh. 7.4 - Finding Confidence Intervals. In Exercises 9-16,...Ch. 7.4 - Prob. 13BSCCh. 7.4 - Prob. 14BSCCh. 7.4 - Prob. 15BSCCh. 7.4 - Prob. 16BSCCh. 7.4 - Prob. 17BSCCh. 7.4 - Prob. 18BSCCh. 7.4 - Determining Sample Size. In Exercises 19-22,...Ch. 7.4 - Prob. 20BSCCh. 7.4 - Prob. 21BSCCh. 7.4 - Prob. 22BSCCh. 7.4 - Prob. 23BBCh. 7 - Prob. 1CQQCh. 7 - Prob. 2CQQCh. 7 - Prob. 3CQQCh. 7 - Prob. 4CQQCh. 7 - Prob. 5CQQCh. 7 - Prob. 6CQQCh. 7 - Prob. 7CQQCh. 7 - Prob. 8CQQCh. 7 - Prob. 9CQQCh. 7 - Prob. 10CQQCh. 7 - 1. Overpaid In a Gallup poll of 557 randomly...Ch. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 1CRECh. 7 - Prob. 2CRECh. 7 - Prob. 3CRECh. 7 - Prob. 4CRECh. 7 - Prob. 5CRECh. 7 - Prob. 6CRECh. 7 - 7. Purell Survey In a survey of 1003 people, 59%...Ch. 7 - Prob. 8CRECh. 7 - Prob. 9CRECh. 7 - Prob. 10CRECh. 7 - Prob. 1FDDCh. 7 - Prob. 2FDDCh. 7 - Prob. 3FDDCh. 7 - Prob. 5FDDCh. 7 - Prob. 6FDD
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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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