00:01
In this question we find the number of people that must be polled in order to find the proportion of the population that support a certain political candidate such that there is a margin of error of 9 % at the 99 % confidence level.
00:18
So if we're drawing a random sample from the population to estimate a population proportion, this estimate for the proportion incurs a margin of error, and assuming that the sample size will be large enough, the margin of error can be calculated as a critical value, z sub alpha over 2, times the standard error, which is the square root of the point estimate for proportion, times 1 minus the point estimate, over the sample size.
00:47
So we want this to be 9%, or .09.
00:54
We want to have 99 % confidence.
00:57
This means that alpha is 1 minus .99, which is .01, and therefore the critical value is z sub .005, which is approximately 2 .576.
01:12
We also need an estimate for proportion...