Determining the Minimum Sample SizeYou want to obtain a sample to estimate a populationproportion. You have no reasonable estimate for thepopulation proportion p. You would like to construct a 90%confidence interval so that your interval esimate is within4% of the true population proportion.How large of a sample size is required?n =Do not round mid-calculation. Use a critical value accurateto three decimal places.

Answered: Determining the Minimum Sample Size You…

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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Question

Determining the Minimum Sample Size
You want to obtain a sample to estimate a population
proportion. You have no reasonable estimate for the
population proportion p. You would like to construct a 90%
confidence interval so that your interval esimate is within
4% of the true population proportion.
How large of a sample size is required?
n =
Do not round mid-calculation. Use a critical value accurate
to three decimal places.

Expert Solution

Step 1

A confidence interval is an inference process which is used to estimate the population parameter. The confidence interval of population proportion gives the range of plausible values of the population proportion.

The margin of error for confidence interval of population proportion isc $M E = z_{c r} \sqrt{\frac{p_{0} (1 - p_{0})}{n}}$ , where $z_{c r}$ is the critical z-score, $p_{0}$ estimate for population proportion and n is sample size. The margin of error is the error by which the estimated can differ from true proportion.