Answer to Question #107190 in Statistics and Probability for jasmine

Question

You are working for a certain candidate who is running a provincial election. This candidate finds out that you have taken a statistics course from a certain statistics professor, and assumes that you know a bit about statistics and sampling. The candidate asks you to take a poll in order to estimate the proportion of the voters who cast their vote for him/her with a margin of error of 0.035. You take it upon yourself to take a simple random sample of n voters. How many samples do you need for a 90% confidence interval. Assume that a recent survey showed 47% of voters have supported him/her.

Answer 1

$ME=z_{0.05}\sqrt{\frac{p(1-p)}{n}}$

$n=(\frac{z_{0.05}}{ME})^2p(1-p)=(\frac{1.645}{0.035})^20.47(1-0.47)=551.$

551 samples are needed.