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For polling firm survey on voters, the smallest sample size which is required to obtain the desired margin of error, is 1850.
What is margin of error?
The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.
[tex]MOE=z\times\dfrac{\sigma}{\sqrt{n}}[/tex]
Here, z is the critical value and n is the sample size.
Here, a polling firm wants to use a one-sample z interval to estimate, the number of proportion of voters in a country plan on voting for a certain candidate.
The margin of error for this test is 3% or 0.03 and the confidence interval is 99 percent.
The z value on the confidence interval of 99 percent is 2.576. Here, the standard deviation for this survey is 50 percent, or 0.50.
Put the value in the above formula as,
[tex]0.03=(2.576)\times\dfrac{0.5}{\sqrt{n}}\\n\approx1850[/tex]
Hence, for polling firm survey on voters, the smallest sample size which is required to obtain the desired margin of error, is 1850.
Learn more about the margin of error here;
https://brainly.com/question/10218601
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