Statistics
13th Edition
ISBN: 9780135820100
Author: MCCLAVE, James T., Sincich, Terry
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 14.5, Problem 67ACB
a.
To determine
Find the rank for all 28 observations.
b.
To determine
Find the sum of ranks for the observations from group 1.
c.
To determine
Find the sum of ranks for the observations from group 2.
d.
To determine
Find the sum of ranks for the observations from group 3.
e.
To determine
Find the Kruskal-Wallis H-statistic using ranks.
f.
To determine
Compare the distributions of number of word pairs recalled for the three groups.
g.
To determine
Compare the word recall distributions of group 1 and group 2 using Wilcoxon rank sum test.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
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 14 Solutions
Statistics
Ch. 14.2 - Prob. 1UPCh. 14.2 - Prob. 2UPCh. 14.2 - Prob. 3LMCh. 14.2 - Prob. 4LMCh. 14.2 - Prob. 5LMCh. 14.2 - Music performance anxiety. Refer to the British...Ch. 14.2 - Prob. 7ACBCh. 14.2 - 15.8 Caffeine in Starbucks coffee. Researchers at...Ch. 14.2 - Emotional empathy in young adults. Refer to the...Ch. 14.2 - Prob. 10ACB
Ch. 14.2 - Prob. 11ACBCh. 14.2 - Prob. 12ACICh. 14.2 - 15.10 Lobster trap placement. Refer to the...Ch. 14.2 - Prob. 14ACICh. 14.2 - Prob. 15ACICh. 14.2 - Prob. 16ACICh. 14.2 - Prob. 17ACICh. 14.3 - What is a rank sum?
Ch. 14.3 - Prob. 19UPCh. 14.3 - Prob. 20UPCh. 14.3 - Prob. 21LMCh. 14.3 - 15.17 Suppose you want to compare two treatments,...Ch. 14.3 - Prob. 23LMCh. 14.3 - Random samples of sizes n1 = 16 and n2 = 12 were...Ch. 14.3 - 15.18 Independent random samples are selected from...Ch. 14.3 - Prob. 26ACBCh. 14.3 - Prob. 27ACBCh. 14.3 - Prob. 28ACBCh. 14.3 - 15.23 The X-Factor in golf performance. Many golf...Ch. 14.3 - Prob. 30ACBCh. 14.3 - Prob. 31ACBCh. 14.3 - 15.85 Children’s recall of TV ads. Refer to the...Ch. 14.3 - Prob. 33ACICh. 14.3 - Prob. 34ACICh. 14.3 - Prob. 35ACICh. 14.3 - Prob. 36ACICh. 14.3 - Prob. 37ACICh. 14.3 - Prob. 38ACICh. 14.3 - Prob. 39ACICh. 14.4 - Explain the difference between the one- and...Ch. 14.4 - Prob. 41UPCh. 14.4 - Prob. 42LMCh. 14.4 - Prob. 43LMCh. 14.4 - Prob. 44LMCh. 14.4 - Prob. 45LMCh. 14.4 - A random sample of nine pairs of measurements is...Ch. 14.4 - Prob. 47ACBCh. 14.4 - Prob. 48ACBCh. 14.4 - Prob. 49ACBCh. 14.4 - Prob. 50ACBCh. 14.4 - Reading comprehension strategies of elementary...Ch. 14.4 - Prob. 52ACBCh. 14.4 - Prob. 53ACICh. 14.4 - Prob. 54ACICh. 14.4 - Prob. 55ACICh. 14.4 - Neurological impairment of POWs. Eleven prisoners...Ch. 14.4 - Prob. 57ACICh. 14.4 - Prob. 58ACACh. 14.5 - 15.43 Under what circumstances does the χ2...Ch. 14.5 - Which of the following results would lead you to...Ch. 14.5 - Suppose you want to use the Kruskal-Wallis H-test...Ch. 14.5 - Data were collected from three populations—A, B...Ch. 14.5 - 15.46 Containing wildfires. The International...Ch. 14.5 - 15.47 Road safety of neighborhoods. The Canadian...Ch. 14.5 - Dog behavior on walks. A field study was conducted...Ch. 14.5 - 15.49 Improving driving performance while...Ch. 14.5 - Effect of scopolamine on memory. Refer to the...Ch. 14.5 - 15.48 Commercial eggs produced from different...Ch. 14.5 - 15.50 Relieving pain with hypnosis. Rehabilitation...Ch. 14.5 - Energy expenditure of laughter. Refer to the...Ch. 14.5 -
Restoring self-control when intoxicated. Refer...Ch. 14.5 - Ground water contamination of wells. Refer to the...Ch. 14.5 - The “name game.” Refer to the Journal of...Ch. 14.5 -
Is honey a cough remedy? Refer to the Archives...Ch. 14.6 - Which of the following statements correctly...Ch. 14.6 - What conditions are required for a valid...Ch. 14.6 - Data were collected under a randomized block...Ch. 14.6 - 15.55 Suppose you have used a randomized block...Ch. 14.6 - 15.56 An experiment was conducted using a...Ch. 14.6 - A new method of evaluating health care research...Ch. 14.6 - Prob. 81ACBCh. 14.6 - 15.64 Containers designed to cool citrus fruit....Ch. 14.6 - 15.57 Estimating time needed to complete a task....Ch. 14.6 - 15.60 Taste testing scales. Refer to the Journal...Ch. 14.6 - Impact study of distractions while driving. The...Ch. 14.6 - 15.58 Condit ions impeding farm production. A...Ch. 14.6 - “Topsy-turvy” seasons in college football. Refer...Ch. 14.6 - 15.65 Irrelevant facial similarity effects on...Ch. 14.6 - Effect of massage on boxers. Refer to the British...Ch. 14.6 - Plants and stress reduction. Refer to the Kansas...Ch. 14.7 - What is the value of rS when there is perfect...Ch. 14.7 - What conditions are required for a valid...Ch. 14.7 - 15.66 Use Table XIV at the end of this chapter to...Ch. 14.7 - 15.67 Specify the rejection region for Spearman’s...Ch. 14.7 - 15.69 Compute Spearman s rank correlation...Ch. 14.7 - 15.68 The following sample data were collected on...Ch. 14.7 - Measuring the moon’s orbit. Refer to the American...Ch. 14.7 - Mongolian desert ants. Refer to the Journal of...Ch. 14.7 - Game performance of water polo players. Refer to...Ch. 14.7 - Lobster fishing study. Refer to the Bulletin of...Ch. 14.7 - Effect of massage on boxers. Refer to the British...Ch. 14.7 - Childhood obesity study. Refer to the Journal of...Ch. 14.7 - Groundwater contamination of wells. Refer to the...Ch. 14.7 - The “name game.” Refer to the Journal of...Ch. 14.7 - 15.76 Taste testing scales. Refer to the Journal...Ch. 14.7 - 15.75 In business, do nice guys finish first or...Ch. 14.7 - 15.74 Food availability at middle schools. Refer...Ch. 14.7 - Pain empathy and brain activity. Refer to the...Ch. 14.7 - Public perceptions of health risks. Refer to the...Ch. 14 - Prob. 110UPCh. 14 - For each of the following, give the appropriate...Ch. 14 - 15.80 The data for three independent random...Ch. 14 - 15.81 A random sample of nine pairs of...Ch. 14 - 15.82 Two independent random samples produced the...Ch. 14 - 15.83 An experiment was conducted using a...Ch. 14 - Radioactive lichen. Refer to the Lichen...Ch. 14 - Prob. 118ACBCh. 14 - Prob. 119ACBCh. 14 - Prob. 120ACBCh. 14 - Prob. 121ACBCh. 14 - Extending the life of an aluminum smelter pot....Ch. 14 - 15.36 NHTSA new car crash tests. Refer to the...Ch. 14 - Prob. 124ACICh. 14 - Prob. 125ACICh. 14 - Prob. 126ACICh. 14 - Prob. 127ACICh. 14 - Prob. 128ACICh. 14 - Prob. 129ACICh. 14 - Prob. 130ACICh. 14 - Prob. 131ACICh. 14 - Prob. 132ACICh. 14 - Prob. 133ACICh. 14 - Prob. 134ACICh. 14 - Prob. 135ACICh. 14 - Prob. 136ACICh. 14 - Prob. 137ACICh. 14 - Prob. 138CTC
Knowledge Booster
Learn more about
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
- 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
- 3. 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_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
- 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
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License