00:01
So our gallup poll surveyed n is equal to 1012 randomly selected us adults, and the proportion was 0 .53 for the number of us adults that were dissatisfied with the quality of education that students receive in kindergarten through grade 12.
00:28
And they might want to use a normal distribution to construct and interpret a 90 % confidence interval for the true population proportion.
00:47
And we also want to find our standard error.
00:53
So the formula for the confidence interval is going to be p hat plus or minus z alpha over 2 times the square root of p hat times 1 minus p hat over n.
01:18
And this was our p hat, sorry.
01:21
And our alpha here is 10 % because we want a 90 % confidence interval.
01:28
So then z alpha over 2 is going to be the z value that's associated with 5 % or 0 .05 in the tail, which is 1 .645.
01:45
So then our confidence interval is equal to our p hat, which is 0 .53 plus or minus 1 .645 times the square root of 0 .53 times 1 minus 0 .53, which is 0 .47, and then divide by n, which was 1012.
02:20
So then our confidence interval is equal to 0 .53 plus or minus 1 .645 times the square root of 0 .53 times 0 .47 divided by 1012.
02:41
And that is 0 .53 plus or minus 0 .258.
02:53
So my confidence interval has a lower bound of 0 .53 minus 0 .258, which is 0 .272...