Mind on Statistics
5th Edition
ISBN: 9781285463186
Author: Jessica M. Utts, Robert F. Heckard
Publisher: Brooks Cole
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Chapter 1, Problem 1.4E
The risk of getting lung cancer at some point in one’s life for men who have never smoked is about 13 in 1000. The risk for men who smoke is just over 13 times the risk for non smokers. (Source: Villenueve and Lau, 1994)
a. What is the base rate for lung cancer in men over a lifetime?
b. What is the approximate lifetime risk of getting lung cancer for men who smoke?
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Pam, Rob and Sam get a cake that is one-third chocolate, one-third vanilla, and one-third strawberry as shown below. They wish to fairly divide the cake using the lone chooser method. Pam likes strawberry twice as much as chocolate or vanilla. Rob only likes chocolate. Sam, the chooser, likes vanilla and strawberry twice as much as chocolate. In the first division, Pam cuts the strawberry piece off and lets Rob choose his favorite piece. Based on that, Rob chooses the chocolate and vanilla parts. Note: All cuts made to the cake shown below are vertical.Which is a second division that Rob would make of his share of the cake?
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
Chapter 1 Solutions
Mind on Statistics
Ch. 1 - Refer to the data and five-number summaries given...Ch. 1 - A five-number summary for the heights in inches of...Ch. 1 - In recent years, Vietnamese American women have...Ch. 1 - The risk of getting lung cancer at some point in...Ch. 1 - Refer to Case Study 1.3, in which teens were asked...Ch. 1 - Using Case Study 1.6 as an example, explain the...Ch. 1 - A CBS News poll taken in December 2009, asked a...Ch. 1 - A telephone survey of 2000 Canadians conducted...Ch. 1 - In Case Study 1.3, the margin of error for the...Ch. 1 - About how many people would need to be in a random...
Ch. 1 - Prob. 1.11ECh. 1 - Prob. 1.12ECh. 1 - Prob. 1.13ECh. 1 - For each of the studies described, explain whether...Ch. 1 - Prob. 1.15ECh. 1 - Suppose that an observational study showed that...Ch. 1 - A randomized experiment was done in which...Ch. 1 - Explain the distinction between statistical...Ch. 1 - A (hypothetical) study of what people do in their...Ch. 1 - Prob. 1.20ECh. 1 - Refer to Case Study 1.6, in which the relationship...Ch. 1 - Students in a statistics class at Penn State were...Ch. 1 - Prob. 1.23ECh. 1 - Prob. 1.24ECh. 1 - An article in the magazine Science (Service, 1994)...Ch. 1 - Prob. 1.26ECh. 1 - Prob. 1.27ECh. 1 - Prob. 1.28ECh. 1 - Refer to the study in Exercise 1.28, in which...Ch. 1 - Prob. 1.30ECh. 1 - Prob. 1.31ECh. 1 - Prob. 1.32ECh. 1 - Prob. 1.33ECh. 1 - Prob. 1.34ECh. 1 - Refer to Exercise 1.33. The Roper Organization...Ch. 1 - Prob. 1.36ECh. 1 - Prob. 1.37ECh. 1 - Prob. 1.38ECh. 1 - Prob. 1.39ECh. 1 - Prob. 1.40ECh. 1 - Prob. 1.41ECh. 1 - Suppose you were to read the following news story:...Ch. 1 - Refer to Case Study 1.5. Explain what mistakes...Ch. 1 - Refer to Case Study 1.6. Go through the five steps...
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- Theorem 7.2 Suppose that E X = 0 for all k, that Var X = 0} x) ≤ 2P(S>x 1≤k≤n S√2), -S√2). P(max Sk>x) ≤ 2P(|S|>x- 1arrow_forwardThree 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 chooser's declarations are Chooser 1: {s3} and Chooser 2: {s3}, which of the following is a fair division of the cake?arrow_forwardTheorem 1.4 (Chebyshev's inequality) (i) Suppose that Var X x)≤- x > 0. 2 (ii) If X1, X2,..., X, are independent with mean 0 and finite variances, then Στη Var Xe P(|Sn| > x)≤ x > 0. (iii) If, in addition, X1, X2, Xn are identically distributed, then nVar Xi P(|Sn> x) ≤ x > 0. x²arrow_forwardTheorem 2.5 (The Lyapounov inequality) For 0arrow_forwardTheorem 1.6 (The Kolmogorov inequality) Let X1, X2, Xn be independent random variables with mean 0 and suppose that Var Xk 0, P(max Sk>x) ≤ Isk≤n Σ-Var X In particular, if X1, X2,..., X, are identically distributed, then P(max Sx) ≤ Isk≤n nVar X₁ x2arrow_forwardTheorem 3.1 (The Cauchy-Schwarz inequality) Suppose that X and Y have finite variances. Then |EXYarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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