You are a pollster for Senator Hillary Clinton. You wish to estimate her popularity among Chicago residents with a 3% margin of error with 95% confidence. From a pilot study you are told that the standard deviation among Chicago residents is 22%.
a) What sample size will you choose?
b) You take the sample and calculate the result. Senator Clinton is not satisfied with your finding, because she heard that the popularity of her closest competitor is within 1% of the estimate you provided her, and she wants to know if she is ahead. Hence, she wants to know her popularity with more precision. She asks you to increase the confidence level to 99%. You say: “Senator, with all due respect, doing that will probably not solve your problem.” Why do you say this? What do you recommend to do instead?
Would I use this equation for part (a)?
n = pq / (SE)^2
n = sample size
p = proportion of population possessing the major attribute (expressed as a decimal)
q = 1 - p
SE = standard error of the proportion
This is the only equation I could find online, but I'm not sure how I would calculate p. I thought I read that if you don't know p, then set it equal to 0.5, but I could be wrong. Standard error not quite sure how to go about solving with my given data.