You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believethe population proportion is approximately p = 0.78. You would like to be 97% confident that your esimateis within 5% of the true population proportion. How large of a sample size is required?Hint: Video[+]n =

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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Related questions

Question

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

Expert Solution

Step 1: Determine the given data in the question

Let p be the population proportion.

Given that,

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