An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
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Chapter 1.6, Problem 4E
Of all sports, football accounts for the highest incidence of concussion in the United States due to the large number of athletes participating and the nature of the sport. While there is general agreement that concussion incidence can be reduced by making rule changes and teaching proper tackling technique, there remains debate as to whether helmet design may also reduce the incidence of concussion. Rowson et al. (2014) report on a retrospective analysis of head impact data collected between 2005 and 2010 from eight collegiate football teams. Concussion rates for players wearing two types of helmets, Riddell VSR4 and Riddell Revolution, were compared. A total of 1,281,444 head impacts were recorded, from which 64 concussions were diagnosed. The relative risk of sustaining a concussion in a Revolution helmet compared with a VSR4 helmet was 46.1%. This study illustrates that differences in the ability to reduce concussion risk exist between helmet models in football. Although helmet design may never prevent all concussions from occurring in football, evidence illustrates that it can reduce the incidence of this injury.
- a. Identify the population that is of interest to the researchers.
- b. Describe the sample.
- c. What characteristics of the population are of interest to the researchers?
- d. If the sample measurements are used to make inferences about the population characteristics, why is a measure of reliability of the inferences important?
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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
An Introduction to Statistical Methods and Data Analysis
Ch. 1.6 - Hansen (2006) describes a study to assess the...Ch. 1.6 - During 2012, Texas had listed on FracFocus, an...Ch. 1.6 - In 2014, Congress cut $8.7 billion from the...Ch. 1.6 - Of all sports, football accounts for the highest...Ch. 1.6 - During the 2004 senatorial campaign in a large...Ch. 1.6 - An American history professor at a major...
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