00:01
An automobile manufacturer is going to estimate the mean gasoline mileage for its new model.
00:06
We know the standard deviation, we need to know the sample size that we're going to require for our estimate.
00:13
Let's work ahead.
00:14
Let's imagine we know the sample size n.
00:17
We go ahead and we find the sample mean and from this we make a confidence interval to estimate the population mean, the mean of all cars of this model.
00:30
The formula for a confidence interval for a population mean is x your point estimate, plus and minus the margin of error z sigma over root n.
00:42
And here's the estimate.
00:44
Now let's just focus on the margin of error because we have been told this cannot exceed 0 .8.
00:50
So i'm going to set it as less than or equal to 0 .8.
00:54
Now if i solve for n i will know what sample size we require.
00:58
So that's what we're going to do.
01:01
We have too many unknowns right now.
01:03
We need something for sigma, we need something for z.
01:06
Sigma, well we've been given that it's 7 .5.
01:09
So that's population standard deviation.
01:12
Z we get from the level of confidence.
01:17
So our sample is a member of a family, every sample of size n.
01:22
And the sample means vary.
01:23
If you were to plot all of them out you would get an approximately normal distribution because of the central limit theorem...