00:01
So a sample has been taken and a confidence interval made.
00:06
We're told the sample size, n, was 116.
00:09
Out of these, 58 of these students responded yes to using a laptop in class.
00:18
And from this a confidence interval was made.
00:21
0 .409 to 0 .591.
00:28
This is a 95 % confidence interval.
00:31
How would it be different if it were 90 % instead? so this is 95%.
00:36
I'm going to write out the formula for a confidence interval for a population proportion.
00:42
It's p -hat, the sample proportion, the point estimate, plus and minus the margin of error.
00:50
Z root p -hat, 1 minus p -hat, over n.
00:56
So p -hat is the proportion of the sample who said yes.
01:00
X over n.
01:02
58 over 116, 0 .5.
01:04
Exactly 50 % of them.
01:07
So this is 0 .5 plus and minus the margin of error found by this.
01:15
This bit is called the standard error.
01:19
This is the critical value.
01:21
The critical value is the part that depends on the level of confidence.
01:25
And where does it come from? well, this is currently a binomial experiment.
01:30
We have n independent trials, two outcomes, they say yes or no.
01:34
Same probability p, whatever it is, of them saying yes.
01:39
In this particular case, 58 successes in this binomial.
01:43
But we don't leave it as a binomial.
01:46
We take a normal approximation, we divide it all by n, so now it represents not x, but x over n, the possible sample proportions you might get...