Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
6th Edition
ISBN: 9781337115186
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
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Chapter 9.3, Problem 19E
The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated with taxpayer calls and has redesigned its phone service as well as posting answers to frequently asked questions on its website (The Cincinnati Enquirer, January 7, 2010). According to a report by a taxpayer advocate, callers using the new system can expect to wait on hold for an unreasonably long time of 12 minutes before being able to talk to an IRS employee. Suppose you select a sample of 50 callers after the new phone service has been implemented; the sample results show a
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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 9 Solutions
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
Ch. 9.1 - 1. The manager of the Danvers-Hilton Resort Hotel...Ch. 9.1 - 2. The manager of an automobile dealership is...Ch. 9.1 - 3. A production line operation is designed to fill...Ch. 9.1 - 4. Because of high production-changeover time and...Ch. 9.2 - 5. Duke Energy reported that the cost of...Ch. 9.2 - Prob. 6ECh. 9.2 - Carpet Salesperson Salaries. Carpetland...Ch. 9.2 - 8. Suppose a new production method will be...Ch. 9.3 - Consider the following hypothesis test:
A sample...Ch. 9.3 - Prob. 10E
Ch. 9.3 - Consider the following hypothesis test:
A sample...Ch. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Federal Tax Returns. According to the IRS,...Ch. 9.3 - In a study entitled How Undergraduate Students Use...Ch. 9.3 - The mean hourly wage for employees in...Ch. 9.3 - Young millennials, adults aged 18 to 34, are...Ch. 9.3 - The Internal Revenue Service (IRS) provides a...Ch. 9.3 - Prescription Drug Costs. Annual expenditure for...Ch. 9.3 - Cost of Telephone Surveys. Fowle Marketing...Ch. 9.3 - Time in Supermarket Checkout Lines. CCN and...Ch. 9.4 - Consider the following hypothesis test:
A sample...Ch. 9.4 - Consider the following hypothesis test:
A sample...Ch. 9.4 - Consider the following hypothesis test:
A sample...Ch. 9.4 - Prob. 26ECh. 9.4 - Which is cheaper: eating out or dining in? The...Ch. 9.4 - CEO Tenure. A shareholders’ group, in lodging a...Ch. 9.4 - The national mean annual salary for a school...Ch. 9.4 - Time in Child Care. The time married men with...Ch. 9.4 - Chocolate Consumption. The United States ranks...Ch. 9.4 - Used Car Prices. According to the National...Ch. 9.4 - Automobile Insurance Premiums. The Onsure.com...Ch. 9.4 - Prob. 34ECh. 9.5 - Consider the following hypothesis test:
A sample...Ch. 9.5 - Prob. 36ECh. 9.5 - The U.S. Bureau of Labor Statistics reports that...Ch. 9.5 - Attitudes toward Supermarket Brands. A study by...Ch. 9.5 - Prob. 39ECh. 9.5 - Prob. 40ECh. 9.5 - Ten years ago 53% of American families owned...Ch. 9.5 - Returned Merchandise. According to the University...Ch. 9.5 - Prob. 43ECh. 9.5 - Prob. 44ECh. 9.5 - The American Association of Individual Investors...Ch. 9.6 - A large department of the Federal Government wants...Ch. 9.6 - CEOs who belong to a popular business-oriented...Ch. 9.6 - Prob. 48ECh. 9.6 - Prob. 49ECh. 9 - Production Line Fill Weights. A production line...Ch. 9 - Scholarship Examination Scores. At Western...Ch. 9 - Exposure to Background Television. CNN reports...Ch. 9 - The Wall Street Journal reported that bachelor’s...Ch. 9 - Data from the Office for National Statistics show...Ch. 9 - The mean time to earn a bachelor’s degree is 5.8...Ch. 9 - Prob. 56SECh. 9 - In Hamilton County, Ohio, the mean number of days...Ch. 9 - Fifty-two percent of Americans report that they...Ch. 9 - Prob. 59SECh. 9 - Prob. 60SECh. 9 - The unemployment rate for 18- to 34-year-olds was...Ch. 9 - Prob. 62SECh. 9 - In recent years more people have been working past...Ch. 9 - Case Problem 1 Quality Associates, Inc.
Quality...Ch. 9 - Case problem 2 Ethical Behavior of Business...
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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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