Statistics for Business & Economics, Revised (with XLSTAT Education Edition Printed Access Card)
13th Edition
ISBN: 9781337094160
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
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Chapter 9.4, Problem 34E
Joan’s Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for the planting of a medium-sized tree. Actual times from a sample of 10 plantings during the past month follow (times in hours).
With a .05 level of significance, test to see whether the
- a. State the null and alternative hypotheses.
- b. Compute the sample mean.
- c. Compute the sample standard deviation.
- d. What is the p-value?
- e. What is your conclusion?
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Students have asked these similar questions
4. Suppose that P(X = 1) = P(X = -1) = 1/2, that Y = U(-1, 1) and that X
and Y are independent.
(a) Show, by direct computation, that X + Y = U(-2, 2).
(b) Translate the result to a statement about characteristic functions.
(c) Which well-known trigonometric formula did you discover?
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
Chapter 9 Solutions
Statistics for Business & Economics, Revised (with XLSTAT Education Edition Printed Access Card)
Ch. 9.1 - The manager of the Danvers-Hilton Resort Hotel...Ch. 9.1 - The manager of an automobile dealership is...Ch. 9.1 - A production line operation is designed to fill...Ch. 9.1 - Because of high production-changeover time and...Ch. 9.2 - Duke Energy reported that the cost of electricity...Ch. 9.2 - The label on a 3-quart container of orange juice...Ch. 9.2 - Carpetland salespersons average 8000 per week in...Ch. 9.2 - Suppose a new production method will be...Ch. 9.3 - consider the following hypothesis test: H0: 20...Ch. 9.3 - Consider the following hypothesis test: H0: 25...
Ch. 9.3 - Consider the following hypothesis test: H0: = 15...Ch. 9.3 - Consider the following hypothesis test: H0: 80...Ch. 9.3 - Consider the following hypothesis test: H0: 50...Ch. 9.3 - Consider the following hypothesis test: H0: = 22...Ch. 9.3 - Individuals filing federal income tax returns...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 - Annual expenditure for prescription drugs was 838...Ch. 9.3 - Fowle Marketing Research, Inc., bases charges to a...Ch. 9.3 - CCN and ActMedia provided a television channel...Ch. 9.4 - Consider the following hypothesis test: H0: 12...Ch. 9.4 - Consider the following hypothesis test: H0: = 18...Ch. 9.4 - Consider the following hypothesis test: H0: 45...Ch. 9.4 - Consider the following hypothesis test: H0: = 100...Ch. 9.4 - Which is cheaper: eating out or dining in? The...Ch. 9.4 - A shareholders group, in lodging a protest,...Ch. 9.4 - The national mean annual salary for a school...Ch. 9.4 - The time married men with children spend on child...Ch. 9.4 - The Coca-Cola Company reported that the mean per...Ch. 9.4 - According to the National Automobile Dealers...Ch. 9.4 - The mean annual premium for automobile insurance...Ch. 9.4 - Joans Nursery specializes in custom-designed...Ch. 9.5 - Consider the following hypothesis test: H0: p =...Ch. 9.5 - Consider the following hypothesis test: H0: p .75...Ch. 9.5 - The U.S. Bureau of Labor Statistics reports that...Ch. 9.5 - A study by Consumer Reports showed that 64% of...Ch. 9.5 - What percentage of the population live in their...Ch. 9.5 - Last year, 46% of business owners gave a holiday...Ch. 9.5 - Ten years ago 53% of American families owned...Ch. 9.5 - According to the University of Nevada Center for...Ch. 9.5 - Eagle Outfitters is a chain of stores specializing...Ch. 9.5 - One of the reasons health care costs have been...Ch. 9.5 - The American Association of Individual Investors...Ch. 9.6 - consider the following hypothesis test. H0: 10...Ch. 9.6 - Consider the following hypothesis test. H0: = 20...Ch. 9.6 - Fowle Marketing Research, Inc., bases charges to a...Ch. 9.6 - A consumer research group is interested in testing...Ch. 9.6 - Young Adult magazine states the following...Ch. 9.6 - Refer to exercise 48. Assume the firm selects a...Ch. 9.6 - Sparr Investments, Inc., specializes in...Ch. 9.7 - Consider the following hypothesis test. H0: 10...Ch. 9.7 - Consider the following hypothesis test. H0: = 20...Ch. 9.7 - Suppose the project director for the Hilltop...Ch. 9.7 - A special industrial battery must have a life of...Ch. 9.7 - Young Adult magazine states the following...Ch. 9.7 - An automobile mileage study tested the following...Ch. 9 - A production line operates with a mean filling...Ch. 9 - At Western University the historical mean of...Ch. 9 - Young children in the United States are exposed to...Ch. 9 - The Wall Street Journal reported that bachelors...Ch. 9 - Data from the Office for National Statistics show...Ch. 9 - A recent issue of the AARP Bulletin reported that...Ch. 9 - The chamber of commerce of a Florida Gulf coast...Ch. 9 - In Hamilton County, Ohio, the mean number of days...Ch. 9 - On December 25, 2009, an airline passenger was...Ch. 9 - An airline promotion to business travelers is...Ch. 9 - Members of the millennial generation are...Ch. 9 - The unemployment rate for 18- to 34-year-olds was...Ch. 9 - A radio station in Myrtle Beach announced that at...Ch. 9 - In recent years more people have been working past...Ch. 9 - Shorney Construction Company bids on projects...Ch. 9 - A federal funding program is available to...Ch. 9 - H0: = 120 and Ha: 120 are used to test whether...Ch. 9 - Quality Associates, Inc. Quality Associates, Inc.,...Ch. 9 - Ethical Behavior of Business Students at Bayview...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- 2,3, ample and rical t? 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?arrow_forward27 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_forward
- 5. 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_forward6. 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_forward
- 8. 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_forward3. Prove that, for any random variable X, the minimum of E(X - a)² is attained for a = EX. Provedarrow_forward7. Cantelli's inequality. Let X be a random variable with finite variance, o². (a) Prove that, for x ≥ 0, P(X EX2x)≤ 02 x² +0² 202 P(|X - EX2x)<≤ (b) Find X assuming two values where there is equality. (c) When is Cantelli's inequality better than Chebyshev's inequality? (d) Use Cantelli's inequality to show that med (X) - EX ≤ o√√3; recall, from Proposition 6.1, that an application of Chebyshev's inequality yields the bound o√√2. (e) Generalize Cantelli's inequality to moments of order r 1.arrow_forward
- The 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_forwardThe 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_forward
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