Suppose you are told that among Atlantic salmons, the proportion of salmons suffering from a viral infection is 0.085. If you collect a sample 250 Atlantic salmons, what is the chance that the proportion of salmons in your sample suffering from a viral infection will be less than 0.9? Would you expect the probability of the event in (1) to be higher or lower if you had a sample of 500 salmons instead? Justify.

Answered: Suppose you are told that among…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose you are told that among Atlantic salmons, the proportion of salmons suffering from a viral infection is 0.085.

If you collect a sample 250 Atlantic salmons, what is the chance that the proportion of salmons in your sample suffering from a viral infection will be less than 0.9?
Would you expect the probability of the event in (1) to be higher or lower if you had a sample of 500 salmons instead? Justify.

Expert Solution

Step 1

Given information:

$\begin{array}{rcl} The proportion of salmons suffering from a viral infection & = & p \\ = & 0.085 \end{array}$

$\hat{p} = 0.90$

n = 250

The sampling distribution of proportion can be approximated by normal distribution:

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