Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
Chapter 15.4, Problem 12E
The accompanying table gives the scores of a group of 15 students in mathematics and art.
- a Use Wilcoxon’s signed-rank test to determine if the locations of the distributions of scores for these students differ significantly for the two subjects. Give bounds for the p-value and indicate the appropriate conclusion with α = .05.
- b State specific null and alternative hypotheses for the test that you conducted in part (a).
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Three players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3).
If the choosers' declarations are Chooser 1: {s1 , s2} and Chooser 2: {s2 , s3}.
Using the lone-divider method, how many different fair divisions of this cake are possible?
Theorem 2.6 (The Minkowski inequality)
Let p≥1. Suppose that X and Y are random variables, such that E|X|P <∞ and
E|Y P <00. Then
X+YpX+Yp
Theorem 1.2 (1) Suppose that P(|X|≤b) = 1 for some b > 0, that EX = 0, and
set Var X = 0². Then, for 0 0,
P(X > x) ≤e-x+1²²
P(|X|>x) ≤2e-1x+1²²
(ii) Let X1, X2...., Xn be independent random variables with mean 0, suppose
that P(X ≤b) = 1 for all k, and set oσ = Var X. Then, for
x > 0.
and
0x) ≤2 exp
Σ
k=1
(iii) If, in addition, X1, X2, X, are identically distributed, then
P(S|x) ≤2 expl-tx+nt²o).
Chapter 15 Solutions
Mathematical Statistics with Applications
Ch. 15.3 - What significance levels between = .01 and = .15...Ch. 15.3 - Prob. 2ECh. 15.3 - Clinical data concerning the effectiveness of two...Ch. 15.3 - Prob. 4ECh. 15.3 - New food products are frequently subjected to...Ch. 15.3 - On clear, cold nights in the central Florida...Ch. 15.3 - A psychological experiment was conducted to...Ch. 15.3 - Refer to Exercise 12.15. Using the sign test, do...Ch. 15.3 - Prob. 9ECh. 15.4 - The accompanying table gives the scores of a group...
Ch. 15.4 - Refer to Exercise 15.4. What answers are obtained...Ch. 15.4 - Refer to Exercise 15.6(a). Answer the question by...Ch. 15.4 - Eight subjects were asked to perform a simple...Ch. 15.4 - Two methods, A and B, for controlling traffic were...Ch. 15.4 - Dental researchers have developed a new material...Ch. 15.4 - Refer to Exercise 12.16. With = .01, use the...Ch. 15.4 - Suppose that Y1, Y2,, Yn is a random sample from a...Ch. 15.4 - The spokesperson for an organization supporting...Ch. 15.6 - Find the p-values associated with each of the...Ch. 15.6 - In some tests of healthy, elderly men, a new drug...Ch. 15.6 - Two plastics, each produced by a different...Ch. 15.6 - Prob. 24ECh. 15.6 - Prob. 25ECh. 15.6 - Prob. 26ECh. 15.6 - Prob. 27ECh. 15.6 - Prob. 28ECh. 15.7 - The table that follows contains data on the leaf...Ch. 15.7 - Prob. 30ECh. 15.7 - Three different brands of magnetron tubes (the key...Ch. 15.7 - An experiment was conducted to compare the length...Ch. 15.7 - Prob. 33ECh. 15.7 - Prob. 34ECh. 15.7 - Prob. 35ECh. 15.8 - In a study of palatability of antibiotics for...Ch. 15.8 - Prob. 38ECh. 15.8 - Prob. 39ECh. 15.8 - A serious drought-related problem for farmers is...Ch. 15.8 - Prob. 41ECh. 15.8 - Prob. 42ECh. 15.8 - Prob. 43ECh. 15.8 - Prob. 44ECh. 15.8 - Prob. 45ECh. 15.9 - Prob. 46ECh. 15.9 - Prob. 47ECh. 15.9 - Prob. 48ECh. 15.9 - Prob. 49ECh. 15.9 - Prob. 50ECh. 15.9 - Prob. 52ECh. 15.10 - Prob. 53ECh. 15.10 - Prob. 54ECh. 15.10 - Prob. 55ECh. 15.10 - Prob. 56ECh. 15.10 - Prob. 57ECh. 15.10 - Prob. 58ECh. 15.10 - Refer to Exercise 11.4. Regard both book and...Ch. 15.10 - Prob. 60ECh. 15 - Prob. 62SECh. 15 - Prob. 63SECh. 15 - Prob. 64SECh. 15 - Prob. 65SECh. 15 - Prob. 67SECh. 15 - Prob. 69SECh. 15 - Prob. 70SECh. 15 - Prob. 71SECh. 15 - Prob. 72SECh. 15 - Prob. 74SECh. 15 - Prob. 75SECh. 15 - Prob. 76SECh. 15 - Prob. 77SECh. 15 - Prob. 78SE
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