00:01
There was a medical rehab education foundation.
00:02
They report that the average cost of rehab for stroke victims is $24 ,672.
00:08
To see if the average cost of rehab is different than a particular hospital, the researchers sampled, randomly sampled, n equals 35 stroke victims in a hospital and found that their average rehab cost was this, $26 ,343.
00:25
And we're told that sigma, the standard deviation of the population is 3 ,251.
00:30
And then we want to know at the alpha of 0 .01 level of significance, that the average stroke rehab at this particular hospital is greater than this value.
00:43
So that is our, that's going to define our hypotheses.
00:46
So our null hypothesis is that the mean is equal to this population mean, 24 ,672.
00:54
We see that the value, the mean of the sample is greater.
00:58
The question is, is it significantly greater? the alternative being mu greater than 24 ,674, excuse me, 672.
01:06
So we're going to use the critical value approach to test this.
01:11
And we're going to make a nice little confidence interval to answer this question.
01:16
All right.
01:16
So let's go ahead and get our critical value.
01:19
Well, the z score that corresponds with this alpha is 2 .33.
01:25
And let me draw a picture of it.
01:27
I think pictures are wonderful.
01:28
So here's our distribution.
01:30
And we should say it's a z distribution because we have a sample size greater than 30.
01:39
And we know the population is standard deviation.
01:41
Therefore, it's a z distribution.
01:43
So here's the z score of 0 right in the center, which corresponds with the mean.
01:46
We want to know if we're significantly above this number.
01:50
And that 2 .33 z score defines our critical region.
01:57
And we're looking for a z score from our test statistic that falls in this critical region here.
02:03
All right.
02:06
So let's go ahead and do that.
02:08
The formula is as follows.
02:10
Z sub x bar is equal to x bar minus the mean of the sampling distribution, which is the mean of the population.
02:20
That's the same thing.
02:21
Mu sub x bar is the same thing as mu.
02:23
Divided by, you might see it as sigma sub x bar, but computationally, that means sigma divided by the square root of n.
02:31
So we have all those values, 26 ,343 minus 24 ,672, all over 3 ,251 divided by root 35.
02:46
And that gets us our z score of 3 .04, which falls in our critical region.
02:53
Here's 2 .33...