00:01
So we have a sample of size 1012.
00:07
We have 552 people who responded yes.
00:12
So our sample proportion is 552 over 1012.
00:18
And we want to use 90 % confidence in our level.
00:24
So alpha is 1 minus 90 % is 10%.
00:28
And we want to find the best point estimate for the population proportion in part a.
00:36
Well, i already did that.
00:37
P hat is 552 over 1012.
00:43
And that gives us, let's see here, 552 divided by 1012.
00:50
Our point estimate is 0 .54545.
00:58
And we went around to three decimal places.
01:02
So that is 0 .545.
01:07
Now for b, we want the margin of error.
01:11
Well, the margin of error is z alpha over 2 times the square root of p hat times 1 minus p hat over n.
01:23
So that is equal to our alpha over 2 is 0 .05.
01:31
And that z value with 0 .05 in the tail is 1 .645.
01:36
So the margin of error is 1 .645 times the square root of 0 .545 times 1 minus 0 .545 divided by n.
01:54
And it is all within the square root...