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 1E
Hansen (2006) describes a study to assess the migration and survival of salmon released from fish farms located in Norway. The mingling of escaped farmed salmon with wild salmon raises several concerns. First, the assessment of the abundance of wild salmon stocks will be biased if there is a presence of large numbers of farmed salmon. Second, potential interbreeding between farmed and wild salmon may result in a reduction in the health of the wild stocks. Third, diseases present in farmed salmon may be transferred to wild salmon. Two batches of farmed salmon were tagged and released in two locations, one batch of 1,996 fish in northern Norway and a second batch of 2,499 fish in southern Norway. The researchers recorded the time and location at which the fish were captured by either commercial fisherman or anglers in fresh water. Two of the most important pieces of information to be determined by the study were the distance from the point of the fish’s release to the point of its capture and the length of time it took for the fish to be captured.
- 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
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