Answered: How's the economy? A pollster wants to…

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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Related questions

Question

How's the economy? A pollster wants to construct a

99.8%

confidence interval for the proportion of adults who believe that economic conditions are getting better.

(a) A poll taken in July

2010

estimates this proportion to be

0.29

. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of

0.03

Expert Solution

Step 1: Given information

The given confidence level is 99.8%

The estimate of population proportion which is sample prorpotion is given as $stack text p end text with hat on top equals 0.29$

it is asked to calculate the required sample size so that confidence interval will have margin of error of 0.03

The formula to calculate the sample size is

$table row cell text n end text end cell equals cell stack text p end text with hat on top space cross times left parenthesis 1 minus stack text p end text with hat on top right parenthesis cross times space open parentheses fraction numerator text z end text subscript c over denominator text ME end text end fraction close parentheses squared end cell end table$

where $stack text p end text with hat on top space equals text Sample proprotion end text$

$text z end text subscript c equals text z critical value end text$

$text ME end text equals space text Margin of error end text$