Loose-leaf For Applied Statistics In Business And Economics
5th Edition
ISBN: 9781259328527
Author: David Doane, Lori Seward Senior Instructor of Operations Management
Publisher: McGraw-Hill Education
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Chapter 2, Problem 51CE
a.
To determine
Identify the sampling method, namely, simple random, systematic, stratified or cluster, that was most likely to have been used in the given situation.
b.
To determine
Identify the sampling method, namely, simple random, systematic, stratified or cluster, that was most likely to have been used in the given situation.
c.
To determine
Identify the sampling method, namely, simple random, systematic, stratified or cluster, that was most likely to have been used in the given situation.
d.
To determine
Identify the sampling method, namely, simple random, systematic, stratified or cluster, that was most likely to have been used in the given situation.
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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
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?
Chapter 2 Solutions
Loose-leaf For Applied Statistics In Business And Economics
Ch. 2.1 - What type of data (categorical, discrete...Ch. 2.1 - What type of data (categorical, discrete...Ch. 2.1 - What type of data (categorical, discrete...Ch. 2.1 - (a) Give three original examples of discrete data,...Ch. 2.1 - Which type of data (cross-sectional or time...Ch. 2.1 - Which type of data (cross-sectional or time...Ch. 2.1 - Prob. 7SECh. 2.1 - Give an original example of a time series variable...Ch. 2.2 - Which measurement level (nominal, ordinal,...Ch. 2.2 - Which measurement level (nominal, ordinal,...
Ch. 2.2 - Which measurement level (nominal, ordinal,...Ch. 2.2 - Which measurement level (nominal, ordinal,...Ch. 2.2 - Vail Resorts uses various types of scales and...Ch. 2.2 - (a) Would the measurement level for the data...Ch. 2.3 - Would you use a sample or a census to measure each...Ch. 2.3 - Would you use a sample or a census to measure each...Ch. 2.3 - The target population is all stocks in the SP 500...Ch. 2.4 - The target population is all students in your...Ch. 2.4 - Prob. 19SECh. 2.4 - Suppose you want to study the number of e-mail...Ch. 2.4 - In Excel, type a list containing names for 10 of...Ch. 2.6 - What sources of error might you encounter if you...Ch. 2.6 - What kind of survey (mail, telephone, interview,...Ch. 2.6 - What kind of survey (mail, telephone, interview,...Ch. 2.6 - Prob. 27SECh. 2.6 - What problems are evident in the wording of these...Ch. 2 - Define (a) data, (b) data set (c) observation, and...Ch. 2 - How do business data differ from scientific...Ch. 2 - Distinguish (a) univariate, bivariate, and...Ch. 2 - Define the four measurement levels and give an...Ch. 2 - Prob. 5CRCh. 2 - (a) List three reasons why a census might be...Ch. 2 - Prob. 7CRCh. 2 - (a) List four methods of random sampling. (b) List...Ch. 2 - List five (a) steps in a survey, (b) issues in...Ch. 2 - Prob. 10CRCh. 2 - Prob. 29CECh. 2 - Prob. 30CECh. 2 - Prob. 31CECh. 2 - Which measurement level (nominal, ordinal,...Ch. 2 - Below are five questions from a survey of MBA...Ch. 2 - Below are five questions from a survey of MBA...Ch. 2 - Below are five questions from a survey of MBA...Ch. 2 - Prob. 36CECh. 2 - Identify the following data as either time series...Ch. 2 - Would you use a sample or a census to measure each...Ch. 2 - Would you use a sample or census to measure each...Ch. 2 - Is each of the following a parameter or a...Ch. 2 - Prob. 41CECh. 2 - Prob. 42CECh. 2 - Prob. 43CECh. 2 - Prob. 44CECh. 2 - The IRS estimates that the average taxpayer spent...Ch. 2 - The General Accounting Office conducted random...Ch. 2 - Arsenic (a naturally occurring, poisonous metal)...Ch. 2 - Prob. 48CECh. 2 - Would you expect Noodles Company to use a sample...Ch. 2 - Prob. 50CECh. 2 - Examine each of the following statistics. Which...Ch. 2 - The National Claims History (NCH) contains records...Ch. 2 - Prior to starting a recycling program, a city...Ch. 2 - A university wanted to survey alumni about their...Ch. 2 - To protect baby scallops and ensure the survival...Ch. 2 - Prob. 56CECh. 2 - Households can sign up for a telemarketing no-call...Ch. 2 - What level of measurement (nominal, ordinal,...Ch. 2 - Insurance companies are rated by several rating...Ch. 2 - A tabletop survey by a restaurant asked the...Ch. 2 - Give two original examples of (a) discrete data...Ch. 2 - Prob. 64CECh. 2 - Below are 64 names of employees at NilCo. Colors...Ch. 2 - From the display below, pick five cards (without...Ch. 2 - Prob. 69CECh. 2 - You can test Excels algorithm for selecting random...
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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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