00:01
Suppose you're a researcher in a hospital, you're experimenting with a new tranquilizer, you collect data on a random set of 12 patients, the period of effectiveness of the tranquilizer for each patient is given, and we're asked to find a point estimate for the population mean length of time, which means we're going to find the sample mean.
00:20
And that sample mean is 2 .55, our sample standard deviation is 0 .3529.
00:31
So they want us to round to four decimal places, but it's 2 .55, so i guess you could put 00 if you really need the four decimal places.
00:41
Which distribution should we use? we're going to use the student t distribution, so t distribution.
00:49
And why? because we have a small sample, and the population standard deviation is unknown.
01:05
What must be true in order to construct a confidence interval in this situation? so the population needs to be approximately normal.
01:18
Since our sample size is so small, the central limit theorem isn't going to be in effect.
01:32
So the population, excuse me, the population from which the sample comes from must be approximately normal.
01:40
So then we're going to construct an 80 percent confidence interval for the population mean length of time.
01:50
And to do that, we need to take t of 0 .20 divided by 2 with a degree of freedom of 11 and find that critical value.
01:59
So you'll need either a t table or online critical value calculator in order to get that critical value.
02:09
And that's going to be 1 .3634.
02:12
So we're going to take our 2 .55 plus or minus 1 .3634 multiplied times 0 .3529 over the square root of 12...