00:01
Here we consider a random sample of 200 residents of la, of which 140 indicated that they voted for the democratic candidate.
00:14
And based on this sample, we were asked to find the standard error and the margin of error at 95 % confidence, as well as the 95 % confidence interval for the proportion of all californians who voted for the democrat.
00:31
Now the standard error is given as the square root of the sample proportion times 1 minus the sample proportion over the sample size.
00:47
Now the sample proportion is x over n.
00:52
For our sample, this comes out to .7.
00:57
And so the standard error is the square root of .7 times .3 over sample size of 200.
01:08
And this comes out to approximately .0635.
01:18
And then for b we are asked for the margin of error.
01:25
And this is equal to, when we have a large sample size like this, a critical value, z subalpha over 2 times the standard error.
01:39
Now since we're looking for 95 % confidence, this means that alpha is 1 minus .95, which is .05...