Essentials of Statistics for Business and Economics
9th Edition
ISBN: 9780357118191
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams
Publisher: Cengage Learning US
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Chapter 7, Problem 66SE
U.S. Drivers and Speeding. ABC News reports that 58% of U.S. drivers admit to speeding. Suppose that a new satellite technology can instantly measure the speed of any vehicle on a U.S. road and determine whether the vehicle is speeding, and this satellite technology was used to take a random sample of 20,000 vehicles at 6 P.M. EST on a recent Tuesday afternoon.
a. For this investigation, what is the sampling distribution for sample proportion of vehicles on U.S. roads that speed?
b. What is the
c. Suppose the sample proportion of speeders
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2 (VaR and ES) Suppose X1
are independent. Prove that
~
Unif[-0.5, 0.5] and X2
VaRa (X1X2) < VaRa(X1) + VaRa (X2).
~
Unif[-0.5, 0.5]
8 (Correlation and Diversification)
Assume we have two stocks, A and B, show that a particular combination
of the two stocks produce a risk-free portfolio when the correlation between
the return of A and B is -1.
9 (Portfolio allocation)
Suppose R₁ and R2 are returns of 2 assets and with expected return and
variance respectively r₁ and 72 and variance-covariance σ2, 0%½ and σ12. Find
−∞ ≤ w ≤ ∞ such that the portfolio wR₁ + (1 - w) R₂ has the smallest
risk.
Chapter 7 Solutions
Essentials of Statistics for Business and Economics
Ch. 7.2 - Consider a finite population with five elements...Ch. 7.2 - Assume a finite population has 350 elements. Using...Ch. 7.2 - Industrial Stock Performance. Fortune publishes...Ch. 7.2 - The 10 most active stocks on the New York Stock...Ch. 7.2 - A student government organization is interested in...Ch. 7.2 - 6. The County and City Data Book, published by the...Ch. 7.2 - 7. Assume that we want to identify a simple random...Ch. 7.2 - Prob. 8ECh. 7.2 - Returns on Mutual Finds. The Wall Street Journal...Ch. 7.2 - 10. Indicate which of the following situations...
Ch. 7.3 - The following data are from a simple random...Ch. 7.3 - Prob. 12ECh. 7.3 - 13. A sample of 5 months of sales data provided...Ch. 7.3 - 14. Morningstar publishes ratings data on 1208...Ch. 7.3 - Rating Wines. According to Wine-Searcher, wine...Ch. 7.3 - AARP Survey. In a sample of 426 U.S. adults age 50...Ch. 7.3 - Attitudes Toward Automation. The Pew American...Ch. 7.5 - 18. A population has a mean of 200 and a standard...Ch. 7.5 - A population has a mean of 200 and a standard...Ch. 7.5 - 20. Assume the population standard deviation is σ...Ch. 7.5 - 21. Suppose a random sample of size 50 is selected...Ch. 7.5 - Sampling Distribution for Electronic Associates,...Ch. 7.5 - Finding Probabilities for Electronic Associates,...Ch. 7.5 - Barrons reported that the average number of weeks...Ch. 7.5 - SAT Scores. In May 2018, The College Board...Ch. 7.5 - Federal Income Tax Returns. The Wall Street...Ch. 7.5 - College Graduate-Level Wages. The Economic Policy...Ch. 7.5 - State Rainfalls. The state of California has a...Ch. 7.5 - Income Tax Return Preparation Fees. The CPA...Ch. 7.5 - To estimate the mean age for a population of 4000...Ch. 7.6 - A sample of size 100 is selected from a population...Ch. 7.6 - 32. A population proportion is .40. A sample of...Ch. 7.6 - Prob. 33ECh. 7.6 - 34. The population proportion is .30. What is the...Ch. 7.6 - Orders from First-Time Customers. The president of...Ch. 7.6 - The Wall Street Journal reported that the age at...Ch. 7.6 - Food Waste. In 2017, the Restaurant Hospitality...Ch. 7.6 - Unnecessary Medical Care. According to Readers...Ch. 7.6 - Better Business Bureau Complaints. In 2016 the...Ch. 7.6 - 40. The Grocery Manufacturers of America reported...Ch. 7.6 - 41. The Food Marketing Institute shows that 17% of...Ch. 7.9 - A population has a mean of 400 and a standard...Ch. 7.9 - Assume the population standard deviation is = 25....Ch. 7.9 - Prob. 44ECh. 7.9 - Assume that the population proportion is .44....Ch. 7.9 - Vacation Hours Earned by Blue-Collar and Service...Ch. 7.9 - MPG for New Cars. The New York Times reported that...Ch. 7.9 - Repeat Purchases. The president of Colossus.com,...Ch. 7.9 - Landline Telephone Service. According to the U.S....Ch. 7 - Shadow Stocks. Jack Lawler, a financial analyst,...Ch. 7 - Personal Health Expenditures. Data made available...Ch. 7 - 44. Foot Locker uses sales per square foot as a...Ch. 7 - Airline Fares. The mean airfare for flights...Ch. 7 - After deducting grants based on need, the average...Ch. 7 - Prob. 55SECh. 7 - Survey Research Results. A researcher reports...Ch. 7 - Production Quality Control. A production process...Ch. 7 - Australians and Smoking. Reuters reports that 15...Ch. 7 - 51. A market research firm conducts telephone...Ch. 7 - Advertisers contract with Internet service...Ch. 7 - The proportion of individuals insured by the...Ch. 7 - Lori Jeffrey is a successful sales representative...Ch. 7 - Life of Compact Fluorescent Lights. In 2018, the...Ch. 7 - Typical Home Internet Usage. According to USC...Ch. 7 - Undeliverable Mail Pieces. Of the 155 billion...Ch. 7 - U.S. Drivers and Speeding. ABC News reports that...Ch. 7 - Managerial Report Prepare a managerial report that...
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- 7 (Multivariate random variable) Suppose X, €1, €2, €3 are IID N(0, 1) and Y2 Y₁ = 0.2 0.8X + €1, Y₂ = 0.3 +0.7X+ €2, Y3 = 0.2 + 0.9X + €3. = (In models like this, X is called the common factors of Y₁, Y₂, Y3.) Y = (Y1, Y2, Y3). (a) Find E(Y) and cov(Y). (b) What can you observe from cov(Y). Writearrow_forward1 (VaR and ES) Suppose X ~ f(x) with 1+x, if 0> x > −1 f(x) = 1−x if 1 x > 0 Find VaRo.05 (X) and ES0.05 (X).arrow_forwardJoy is making Christmas gifts. She has 6 1/12 feet of yarn and will need 4 1/4 to complete our project. How much yarn will she have left over compute this solution in two different ways arrow_forward
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