Question

Determining the Minimum Sample Size A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 3% margin of error at a 90% confidence level, what is the minimum sample size needed for the study? Give your answer as a whole number.

Answer #1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3% = 0.03

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_{/2} = Z_{0.05} =
1.645

Sample size = n = ((Z_{ / 2}) / E)^{2} *
* (1 - )

= (1.645 / 0.03)^{2} * 0.5 * 0.5

= 751.58

n = sample size = 752

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