00:01
We have some information about a confidence interval.
00:03
The actual interval is 0 .1323 up to 0 .4677.
00:12
We are told that the sample size, n, was 50, and p -hat, the sample proportion, was 0 .3.
00:20
That would also be the midpoint of this interval.
00:23
What's the level of confidence? let's look at the formula that you use to construct this interval.
00:28
An interval for a population proportion based on a single sample.
00:33
The formula is p -hat, your point estimate, plus and minus the margin of error, z root p -hat, 1 minus p -hat, over n.
00:46
So p -hat is the midpoint.
00:48
We didn't actually need to be told that.
00:50
We could have found that from the interval by just finding the centre of the interval.
00:53
But we have that, so that's nice.
00:56
We're just going to look at the margin of error.
00:59
We have p -hat, we have n, and then z.
01:02
Z comes from the level of confidence.
01:05
So what is the error? it's whatever i add on to 0 .3 to get the upper bound, or subtract away from it to get the lower bound.
01:12
So i'm just going to look at the upper bound minus p -hat to get 0 .1677.
01:19
You can see that if i add these two together i would get p -hat as well.
01:24
So this is the error.
01:27
What you add on to p -hat to get the upper bound, subtract it below the bound, and it is equal to z root p -hat, 1 minus p -hat, over n.
01:38
So if i take this big thing in the square root sign and divide both sides by that, we can find z.
01:46
I'm going to put these values in, see what z is.
01:50
So i'm going to find the numerator via denominator first.
01:54
So we've got 0 .3 multiplied by 0 .7, divided by 50, square root that.
01:59
Now i'm going to divide the numerator by that value to get z is 2 .58823 decimal places.
02:11
Okay, so that's our critical value.
02:16
Now how does that relate to confidence? for that we need to go to the normal distribution.
02:21
Initially this experiment was a binomial distribution...