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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Textbook Question
Chapter 15.9, Problem 45E
In Table 15.12 we provided estimates of the
- a. Compute the odds in favor of using the coupon for a customer with annual spending of $4000 who does not have a Simmons credit card (x1 = 4, x2 = 0).
- b. Use the information in Table 15.12 and part (a) to compute the odds ratio for the Simmons credit card variable x2 = 0, holding annual spending constant at x1 = 4.
- c. In the text, the odds ratio for the credit card variable was computed using the information in the $2000 column of Table 15.12. Did you get the same value for the odds ratio in part (b)?
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9. The concentration function of a random variable X is defined as
Qx(h) = sup P(x ≤ X ≤x+h), h>0.
x
(a) Show that Qx+b (h) = Qx(h).
(b) Is it true that Qx(ah) =aQx(h)?
(c) Show that, if X and Y are independent random variables, then
Qx+y (h) min{Qx(h). Qy (h)).
To put the concept in perspective, if X1, X2, X, are independent, identically
distributed random variables, and S₁ = Z=1Xk, then there exists an absolute
constant, A, such that
A
Qs, (h) ≤
√n
Some references: [79, 80, 162, 222], and [204], Sect. 1.5.
29
Suppose that a mound-shaped data set has a
must mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 6 and 12?
b. About what percentage of the data should
lie between 4 and 6?
c. About what percentage of the data should
lie below 4?
91002 175/1
3
2,3,
ample
and
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the
28 Suppose that a mound-shaped data set has a
mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 8 and 12?
b. About what percentage of the data should
lie above 10?
c. About what percentage of the data should
lie above 12?
Chapter 15 Solutions
Essentials of Statistics for Business and Economics
Ch. 15.2 - The estimated regression equation for a model...Ch. 15.2 - Consider the following data for a dependent...Ch. 15.2 - 3. In a regression analysis involving 30...Ch. 15.2 - A shoe store developed the following estimated...Ch. 15.2 - Theater Revenue. The owner of Showtime Movie...Ch. 15.2 - NFL Winning Percentage. The National Football...Ch. 15.2 - Rating Computer Monitors. PC Magazine provided...Ch. 15.2 - Scoring Cruise Ships. The Condé Nast Traveler Gold...Ch. 15.2 - House Prices. Spring is a peak time for selling...Ch. 15.2 - Baseball Pitcher Performance. Major League...
Ch. 15.3 - In exercise 1, the following estimated regression...Ch. 15.3 - In exercise 2, 10 observations were provided for a...Ch. 15.3 - 13. In exercise 3, the following estimated...Ch. 15.3 - In exercise 4, the following estimated regression...Ch. 15.3 - Prob. 15ECh. 15.3 - 16. In exercise 6, data were given on the average...Ch. 15.3 - Quality of Fit in Predicting House Prices. Revisit...Ch. 15.3 - R2 in Predicting Baseball Pitcher Performance....Ch. 15.5 - In exercise 1, the following estimated regression...Ch. 15.5 - Refer to the data presented in exercise 2. The...Ch. 15.5 - The following estimated regression equation was...Ch. 15.5 - Testing Significance in Shoe Sales Prediction. In...Ch. 15.5 - Testing Significance in Theater Revenue. Refer to...Ch. 15.5 - Testing Significance in Predicting NFL Wins. The...Ch. 15.5 - Auto Resale Value. The Honda Accord was named the...Ch. 15.5 - Testing Significance in Baseball Pitcher...Ch. 15.6 - In exercise 1, the following estimated regression...Ch. 15.7 - Consider a regression study involving a dependent...Ch. 15.7 - Consider a regression study involving a dependent...Ch. 15.7 - 34. Management proposed the following regression...Ch. 15.7 - Repair Time. Refer to the Johnson Filtration...Ch. 15.7 - Extending Model for Repair Time. This problem is...Ch. 15.7 - Pricing Refrigerators. Best Buy, a nationwide...Ch. 15.9 - In Table 15.12 we provided estimates of the...Ch. 15 - 49. The admissions officer for Clearwater College...Ch. 15 - 50. The personnel director for Electronics...Ch. 15 - A partial computer output from a regression...Ch. 15 - Analyzing College Grade Point Average. Recall that...Ch. 15 - Analyzing Job Satisfaction. Recall that in...Ch. 15 - Analyzing Repeat Purchases. The Tire Rack,...Ch. 15 - Zoo Attendance. The Cincinnati Zoo and Botanical...Ch. 15 - Mutual Fund Returns. A portion of a data set...Ch. 15 - Gift Card Sales. For the holiday season of 2017,...Ch. 15 - Consumer Research, Inc., is an independent agency...Ch. 15 - Matt Kenseth won the 2012 Daytona 500, the most...Ch. 15 - When trying to decide what car to buy, real value...
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- 27 Suppose that you have a data set of 1, 2, 2, 3, 3, 3, 4, 4, 5, and you assume that this sample represents a population. The mean is 3 and g the standard deviation is 1.225.10 a. Explain why you can apply the empirical rule to this data set. b. Where would "most of the values" in the population fall, based on this data set?arrow_forward30 Explain how you can use the empirical rule to find out whether a data set is mound- shaped, using only the values of the data themselves (no histogram available).arrow_forward5. Let X be a positive random variable with finite variance, and let A = (0, 1). Prove that P(X AEX) 2 (1-A)² (EX)² EX2arrow_forward
- 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.arrow_forward4. Prove that, for any random variable X, the minimum of EIX-al is attained for a = med (X).arrow_forward8. 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).arrow_forward
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- The Honolulu Advertiser stated that in Honolulu there was an average of 659 burglaries per 400,000 households in a given year. In the Kohola Drive neighborhood there are 321 homes. Let r be the number of homes that will be burglarized in a year. Use the formula for Poisson distribution. What is the value of p, the probability of success, to four decimal places?arrow_forwardThe college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.arrow_forwardWhat was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Use a histogram and graph the probability distribution. Using the graph of the probability distribution determine the probability that a British nurse selected at random in 1851 would be 40 years of age or older. Round your answer to nearest thousandth. Age range (yr) 20–29 30–39 40–49 50–59 60–69 70–79 80+ Midpoint (x) 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8%arrow_forward
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