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.
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 = Z0.05 = 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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