To estimate a population proportion, you want to obtain a sample. Based on previous evidence, you believe the population proportion is approximately $ p = 0.78 $. You would like to be 97% confident that your estimate is within 5% of the true population proportion. How large of a sample size is required?Hint: Video [+] $ n = $ [Input box]This text provides a context for calculating the sample size required to estimate a population proportion, given a specified confidence level and margin of error. There's a reference to a video hint for additional help, and an input box for entering the calculated sample size.

Answered: the population proportion is…

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

To estimate a population proportion, you want to obtain a sample. Based on previous evidence, you believe the population proportion is approximately $ p = 0.78 $. You would like to be 97% confident that your estimate is within 5% of the true population proportion. How large of a sample size is required?

Hint: Video [+]

$ n = $ [Input box]

This text provides a context for calculating the sample size required to estimate a population proportion, given a specified confidence level and margin of error. There's a reference to a video hint for additional help, and an input box for entering the calculated sample size.

Expert Solution

Step 1: Determine the given data in the question

Let p be the population proportion.

Given that,

$P o p u l a t i o n space p r o p o r t i o n space left parenthesis p right parenthesis equals 0.78 q equals 1 minus p equals 1 minus 0.78 equals 0.22 M a r g i n space o f space e r r o r space left parenthesis E right parenthesis equals 5 percent sign equals 0.05 C o n f i d e n c e space l e v e l space left parenthesis C right parenthesis equals 97 percent sign equals 0.97 alpha equals 1 minus C equals 1 minus 0.97 equals 0.03 1 minus alpha over 2 equals 1 minus fraction numerator 0.03 over denominator 2 end fraction equals 0.985$