00:01
The following is the solution video to number 25, and this looks at a very small data set.
00:04
In fact, there are only four data values of the amount that it costs for repairs for chevy cavaliers.
00:12
And the first part of this asks for a point estimate for the mean.
00:15
And the point estimate for mean is just going to be the sample means, so x bar.
00:19
And we're also assuming that the sigma, the population standard deviation, we know it, is $220.
00:24
So the way you find x bar is just, you know, finding the average, the arithmetic mean.
00:28
So you add them together and divide by four.
00:31
Or you can use technology, and i'm going to use technology.
00:33
So if you go to stat and edit, they're your data values.
00:35
So one of them was $225, $462, $729, and 753.
00:40
And then if you go to stat and then calc, and it's one bar stats, and we're going to make that l1.
00:47
And we calculate that and we get this x bar here, 542 .25.
00:53
Okay, so the point estimate is $542 .25.
01:03
In part b, we're given a box plot and a normal probability plot, and we're basically just checking to make sure that the distribution of the population is approximately normal.
01:15
And looking at those two, it appears to be approximately normal, so the short answer, yes.
01:21
We can use the z interval here, even if the sample size is so small, because the box plot appears that there are no outliers, and the normal probability plot looks like it's about linear.
01:33
So in short, we're just going to say, yes, it's approximately normal.
01:43
The box plot says that there are no outliers.
01:49
And since the normal probability plot is approximately linear, so the normal probability plot is within range, we'll say.
02:06
Which means that none of those data values are kind of outside those lines.
02:10
And then the next couple parts, we're going to go ahead and use our inference procedure, and we're going to find the 95 % confidence interval.
02:17
And i'm going to go back to technology and do that.
02:20
Now you can use the formula for one, but technology is much faster, so i'm going to do that.
02:23
So if you go to stat test, and we're going to use the z interval since we know what the population standard deviation is.
02:28
So it's the seventh option.
02:30
And usually we leave it on stats because we're given summary stats, but this time we're actually given a data set.
02:34
So i want to leave it on data.
02:36
Now the sigma was given to you in the problem.
02:39
It's 220.
02:40
For your list, go ahead and change that to l1.
02:43
Unless you put it in a different column and then put it as l2 or l3 or whatever.
02:47
But i put in l1, and then the frequencies one, and then the c level, the confidence level, is 95%.
02:52
So 0 .95.
02:54
Then we can calculate, and then this first line here, that gives us the 95 % confidence interval.
03:00
So 326 .5 and 757 .85.
03:06
It's between those two...