You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately $ p^* = 36\% $. You would like to be 99.9% confident that your estimate is within 1.5% of the true population proportion. How large of a sample size is required?\[ n = \]Do not round mid-calculation. However, use a critical value accurate to three decimal places.Question Help: Message instructorSubmit Question

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Description: You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately $ p^* = 36\% $. You would like to be 99.9% confident that your estimate is within 1.5% of the true

Answered: You want to obtain a sample to estimate…

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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You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately $ p^* = 36\% $. You would like to be 99.9% confident that your estimate is within 1.5% of the true population proportion. How large of a sample size is required?

\[ n = \]

Do not round mid-calculation. However, use a critical value accurate to three decimal places.

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Step 1

Let p* denote the population proportion.

Given that p*=36%=36/100=0.36

The estimate is within 1.5% of the true population proportion.

That is, E =1.5%=1.5/100=0.015

The confidence interval is given as 99.9%

That is, c=99.9%=99.9/100=0.999

The level of significance is,

$α$ = 1-c=1-0.999=0.001

From standard normal table at $α =$ 0.001 level of significance, the two- tailed critical value is,

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