00:01
For this question, we are interested in finding what sample size is necessary to estimate a population proportion within 0 .03 of the true proportion at 90 % confidence.
00:14
Now, when we're estimating a population proportion from a large enough sample, the confidence interval that we will create is calculated using the sample proportion plus or minus some margin of error.
00:32
So it's this margin of error that we want to be no bigger than 0 .03.
00:36
So once again, assuming the sample size will be large enough, the margin of error is calculated as a critical value, z sub alpha over 2, times standard error, which is the square root of the point estimate for proportion, times 1 minus the point estimate for proportion over the sample size.
01:11
Since we want a 90 % confidence interval, this means that alpha is 1 minus 0 .9, which is 0 .1, and therefore the critical value is z sub 0 .05, which is 1 .645.
01:23
So for rearranging for n, in this inequality we have n must be at least the following...