A political candidate has asked you to conduct a poll to determine what percentage of people support her.

Question

A political candidate has asked you to conduct a poll to determine what percentage of people support her.

If the candidate only wants a 7% margin of error at a 95% confidence level, what size of sample is needed?

Give your answer in whole people.

Answer 1

Since the Confidence Interval=95%, or C=0.95.

Now alpha=(1-C)=(1-0.95)=0.05. hence alpha over 2=0.025

a. z value for alpha/2 (Z sub 0.025) from the Z table =1.96

b. The margin of error E=7%=0.07 ( as stated in the question)

c. p= proportion which is not given. In such a case we assume p=0.5 (or 50%)

The sample size formula is, n = Z_α/2² *p*(1-p) / E^2..

^{Plug in the values in the above formula to get n= 196.}

^{So if the candidate wants 7% margin of error at a 95%confidence level, the sample size needed is 196.}