Problem 71 (a) For the capture-recapture me... [FREE SOLUTION] (2024)

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Chapter 14: Problem 71

(a) For the capture-recapture method to give a reasonable estimate of \(N\),what assumptions about the two samples must be true? (b) Give reasons why the assumptions in (a) may not hold true in manysituations.

Short Answer

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For the capture-recapture method to give a reasonable estimate of \(N\), it must be assumed that each member of the population has an equal chance of being captured in both samples, and that the population size does not change between samples. These assumptions may not hold true due to variation in capture probability among population members and changes in population size between samples, respectively.

Step by step solution

Understand the Assumptions of the Capture-Recapture Method

The capture-recapture method makes two main assumptions. First, it assumes that each member of the population has an equal chance of being captured in both the first and second sample. Second, it assumes that the population size \(N\) does not change between the first and second sample. Both of these assumptions are necessary for the capture-recapture method to give a reasonable estimate of population size.

Consider Why the Assumptions May Not Hold True

Even though the capture-recapture method is a powerful tool for estimating population size, its assumptions do not always hold true. The assumption of equal likelihood of capture may be violated if certain members of the population are more or less likely to be captured than others. For example, some animals may be more elusive or more attracted to traps than others.The assumption of a stable population size may be violated if the population changes between the first and second sample due to births, deaths, migration, or other factors. For example, bird populations might change significantly between seasons due to migration patterns. As such, the timing of sampling could significantly affect the estimate of population size.

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Most popular questions from this chapter

Informal surveys. In everyday life we are constantly involved in activitiesthat can be described as informal surveys, often without even realizing it.Here are some examples. (i) Al gets up in the morning and wants to know what kind of day it is goingto be, so he peeks out the window. He doesn't see any dark clouds, so hefigures it's not going to rain. (ii) Betty takes a sip from a cup of coffee and burns her lips. She concludesthat the coffee is too hot and decides to add a tad of cold water to it. (iii) Carla got her first Math 101 exam back with a C grade on it. Thestudents sitting on each side of her also received C grades. She concludesthat the entire Math 101 class received a \(C\) on the first exam. For each of the preceding examples, (a) describe the population. (b) discuss whether the sample is random or not. (c) discuss the validity of the conclusions drawn. (There is no right or wronganswer to this question, but you should be able to make a reasonable case foryour position.)Refer to a landmark study conducted in 1896 in Denmark by Dr. JohannesFibiger, who went on to receive the Nobel Prize in Medicine in \(1926 .\) Thepurpose of the study was to determine the effectiveness of a new serum fortreating diphtheria, a common and often deadly respiratory disease in thosedays. Fibiger conducted his study over a one-year period (May 1896-April 1897)in one particular Copenhagen hospital. New diphtheria patients admitted to thehospital received different treatments based on the day of admission. In oneset of days (call them "even" days for convenience), the patients were treatedwith the new serum daily and received the standard treatment. Patientsadmitted on alternate days (the "odd" days) received just the standardtreatment. Over the one-year period of the study, eight of the 239 patientsadmitted on the "even" days and treated with the serum died, whereas 30 of the245 patients admitted on the "odd" days died. (a) Describe as specifically as you can the target population for Fibiger'sstudy. (b) Describe the sampling frame for the study.Refer to the following story: The 1250 students at Eureka High School arehaving an election for Homecoming King. The candidates are Tomlinson (captainof the football team), Garcia (class president), and Marsalis (member of themarching band). At the football game a week before the election, a pre-election poll was taken of students as they entered the stadium gates. Of thestudents who attended the game, 203 planned to vote for Tomlinson, 42 plannedto vote for Garcia, and 105 planned to vote for Marsalis. (a) Give the sample statistics estimating the percentage of the vote going toeach candidate. (b) A week after this survey, Garcia was elected Homecoming King with \(51 \%\)of the vote, Marsalis got \(30 \%\) of the vote, and Tomlinson came in last with\(19 \%\) of the vote. Find the sampling errors in the survey expressed aspercentages.Refer to the following story: \(A n\) orange grower wishes to compute theaverage yield from his orchard. The orchard contains three varieties of trees:\(50 \%\) of his trees are of variety \(A, 25 \%\) of variety \(B,\) and \(25 \%\) ofvariety \(C .\) (a) Suppose that in his survey, the grower found that each tree of variety Aaverages 100 oranges, each tree of variety \(\mathrm{B}\) averages 50 oranges,and each tree of variety C averages 70 oranges. Estimate the average yield pertree of his orchard. (b) Is the yield you found in (a) a parameter or a statistic? Explain.Refer to a clinical trial named APPROVe designed to determine whether Vioxx, amedication used for \(a r\) thritis and acute pain, was effective in preventingthe recurrence of colorectal polyps in patients with a history of colorectaladenomas. APPROVe was conducted between 2002 and 2003 and involved 2586participants, all of whom had a history of colorectal adenomas. Theparticipants were randomly divided into two groups: 1287 were given 25milligrams of Vioxx daily for the duration of the clinical trial (originallyintended to last three years), and 1299 patients were given a placebo. Neitherthe participants nor the doctors involved in the clinical trial knew who wasin which group. During the trial, 72 of the participants had cardiovascularevents (mostly heart attacks or strokes). Later it was found that 46 of thesepeople were from the group taking the Vioxx and only 26 were from the grouptaking the placebo. Based on these results, the clinical trial was stopped in2003 and Vioxx was taken off the market in 2004. (a) Describe the control and treatment groups in APPROVe. (b) APPROVe can be described as a double-blind, randomized controlled placebostudy. Explain why each of these terms applies.

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Problem 71 (a) For the capture-recapture me... [FREE SOLUTION] (2024)

Short Answer

Step by step solution

Understand the Assumptions of the Capture-Recapture Method

Consider Why the Assumptions May Not Hold True

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Applied Mathematics

Pure Maths

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Privacy Overview

References