You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 78%. You would like to be 95% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required?
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 78%. You would like to be 95% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required?
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 78%. You would like to be 95% confident that your estimate is within 1% of the true population proportion. How large of a
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Step 1
Introduction:
The confidence interval for the population proportion, p at the 100 (1 – α) % confidence level is:
Here, n is the sample size, p is the sample proportion, and zα/2 is the upper critical value of the standard normal distribution.
The margin of error in this confidence interval is:
When population proportion, p is known, p̂ will be substituted by the population proportion, p in the expression for E.
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