00:01
A pollster wants to estimate the proportion of adults who believe that economic conditions are getting better.
00:07
They don't know what sample size they need.
00:09
If they did know their sample size, n, they'd go ahead take their sample and find p -hat, the sample proportion.
00:16
From this they would make a confidence interval to estimate the population proportion.
00:22
The formula to do so is p -hat, their point estimate, plus and minus the margin of error, z root p -hat, 1 minus p -hat, over n.
00:33
We're just going to focus on this margin of error since we're told the error should be 0 .037.
00:41
Now if i solve for n, i'll know the sample size necessary to make this true.
00:46
We just have a couple of unknowns first.
00:49
For p -hat, we have been given a prior estimate.
00:52
We think 0 .33 is the population proportion, so that's our planning value to help us get a more accurate answer.
01:01
Z comes from the level of confidence.
01:05
So initially this poll is a binomial experiment.
01:08
N independent trials, two outcomes, they believe this or they don't.
01:11
Same probability p, whatever it is, but they do believe it.
01:16
The binomial variable is x, the number of people in the sample who do believe it...