41. Estimate the fish population of Example 4.3.4, page 144, with a 68%confidence level. Example 4.3.4. We are interested in estimating the population of fish in alake. A sample of 150 fish is caught, tagged, and released back to the lake. Aweek later, a new sample of 100 fish is caught, and the number of tagged fishis found to be 12. What is the number of fish in the lake?The method is based on the observation that if the tagged fish mix wellwith the rest of the population, and the second sample is randomly chosen,then the proportion of tagged fish in the sample will be approximately thesame as the proportion of tagged fish in the population. Thus we have atand thereforeN'proportion of 4 numbersnn·t(4.2)wherer is the number of tagged fish in the (second) sample, that is the number offish recaptured,n is the size of the (second) sample,t is the number of tagged fish in the whole population. That is, the size ofthe first sample,N is the size of the population.In our example we have r =12, п 3100, t = 150 and N is unknown. Weconclude that100 · 150N1250,12i.e. the fish population in the lake is approximately 1,250.

GivenThe number of fish tagged t=150The sample size of fish caught n=100The number of tagged fish…

Answered: Estimate the fish population of Example…

Math

Statistics

Estimate the fish population of Example 4.3.4, page 144, with a 68% confidence level.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

41. Estimate the fish population of Example 4.3.4, page 144, with a 68%
confidence level.

Example 4.3.4. We are interested in estimating the population of fish in a
lake. A sample of 150 fish is caught, tagged, and released back to the lake. A
week later, a new sample of 100 fish is caught, and the number of tagged fish
is found to be 12. What is the number of fish in the lake?
The method is based on the observation that if the tagged fish mix well
with the rest of the population, and the second sample is randomly chosen,
then the proportion of tagged fish in the sample will be approximately the
same as the proportion of tagged fish in the population. Thus we have a
t
and therefore
N'
proportion of 4 numbers
n
n·t
(4.2)
where
r is the number of tagged fish in the (second) sample, that is the number of
fish recaptured,
n is the size of the (second) sample,
t is the number of tagged fish in the whole population. That is, the size of
the first sample,
N is the size of the population.
In our example we have r =
12, п 3
100, t = 150 and N is unknown. We
conclude that
100 · 150
N
1250,
12
i.e. the fish population in the lake is approximately 1,250.

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