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A political candidate has asked you to conduct a poll to determine what percentage of people support her. If thecandidate only wants a 1.5% margin of error at a 99% confidence level, what size of sample is needed?

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A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the
candidate only wants a 1.5% margin of error at a 99% confidence level, what size of sample is needed?
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A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 1.5% margin of error at a 99% confidence level, what size of sample is needed?

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Step 1

Sample size:

The minimum sample size for a desired confidence level, α with a given margin of error, E is given by:

 

n p(1-p)
E
Here, pis the true proportion
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n p(1-p) E Here, pis the true proportion

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Step 2

Computing the sample size:

Thus, it is given that the confidence level is 99%. Therefore, the significance level, α = 0.01.

From the EXCEL, using the formula, = NORM.INV(0.995,0,1), the critical value, zα/2 is 2.576.

That is, the true ...

n p(1-p
E
2.576
(0.5)(1-0.5)0.015
(0.5)(0.5)(29,492.338)
7.374
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n p(1-p E 2.576 (0.5)(1-0.5)0.015 (0.5)(0.5)(29,492.338) 7.374

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Math

Statistics

Hypothesis Testing

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