You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believethe population proportion is approximately 31%. You would like to be 98% confident that your estimate iswithin 3% of the true population proportion. How large of a sample size is required?Submit QuestionIN%3D

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Description: You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believethe population proportion is approximately 31%. You would like to be 98% confident that your estimate iswithin 3% of the true population proporti

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Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 3E

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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 31%. You would like to be 98% confident that your estimate is
within 3% of the true population proportion. How large of a sample size is required?
Submit Question
IN
%3D

Expert Solution

Step 1

Given Information:

Population proportion p = 31% = 0.31

Confidence level = 98% = 0.98

Margin of Error = 3% = 0.03

To obtain a sample to estimate a population proportion:

Sample size can be obtained using the formula:

$n = {(\frac{Z_{α / 2}}{M . E})}^{2} p (1 - p)$

where, $p$ is the prior population proportion

$Z_{α / 2}$ is two tailed z-critical value at significance level $α = \frac{1 - 0.98}{2} = 0.01$

$M . E$ is the margin of error

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