00:01
We're looking at taking a sample and estimating the mean gasoline mileage of a new compact model for an automobile.
00:08
Okay, let's look ahead.
00:10
Let's pretend we know what the sample size needs to be, n, and we go ahead and we find the sample mean, x bar.
00:19
And we take the sample mean and we make a confidence interval.
00:27
The formula for a confidence interval for a population mean is x bar plus and minus z sigma.
00:34
Over root n.
00:37
So this is what they'll use and they'll have their estimates.
00:40
Now i'm just going to focus on the margin of error, because i know this cannot exceed 0 .3.
00:47
So i've set it as less than or equal to 0 .3.
00:50
And now, if i solve for n, i will know how big the sample had to be.
00:56
Okay, but we need something to put in for z and for sigma.
00:59
We have sigma, the population standard deviation, as 1 .5.
01:05
Z, we get a, from a level of confidence.
01:08
So this sample is a member of a family, every sample of this particular size.
01:14
And if you were to plot out the different sample means, they would follow an approximately normal distribution.
01:20
For a competence interval, we put our point estimate in the middle, and we make our interval around it.
01:27
And say, 90 % of the area of this curve is in the interval, we can be 90 % confident that the population mean falls into the interval...