00:01
Okay, doke, let's find a 90 % confidence interval for the number of people who are struggling to find gifts for their friends and family.
00:09
So, to find the 90 % confidence interval, we want to start by finding the margin of error.
00:15
And we're going to use our handy formula, which is e is equal to z, z value, times a square root of whatever p -hat and q -hat make as a product.
00:29
And then we divide it all by n, the size of the total population.
00:35
So when we're looking for a 90 % confidence interval, we can refer back to our useful values.
00:40
Z is going to be 1 .65 rate.
00:46
P, it's the 68 % of people who do, in fact, struggle to find gifts.
00:51
It's going to be 0 .68, and q is going to be 1 minus .68.
00:59
And then how many people do we have in total? that'll be 100.
01:04
And we can just go ahead and plug this into a calculator.
01:13
And what do we get? that'll give us 0 .077...