00:01
All right, this problem is about 84 used cars.
00:05
It's a sample, so our n value is going to be 84.
00:09
And they gave us some more data on the sample.
00:12
They told us the sample mean was $6 ,425, and they told us the sample standard deviation was $3 ,156 .00.
00:29
This problem does come in four different parts, and when we get to part c, there's parts within part c.
00:37
So let's tackle part a.
00:40
Part a is asking us which distribution should you use for this problem? and you should be using the student's t distribution.
00:53
And the reason we are using the student's t distribution is because we do not know the population standard deviation.
01:21
We do have a standard deviation that was provided us, but it is referring back to the sample of 84 used cars.
01:29
So because we do not know the population standard deviation, we will use the student's t distribution.
01:37
For part b, it's asking us to define the variable x bar in words.
01:44
So x bar is going to represent the mean cost of the 84 used cars.
02:08
Now for part c, there are three parts to it, and i'm going to tackle them a little out of order.
02:17
So in part c, it's asking us to come up with the confidence interval, to sketch the graph, and to calculate the error bound.
02:26
In order to come up with the confidence interval, we do have to find the error bound first.
02:31
So let's tackle that.
02:33
So we are trying to come up with a confidence interval at the 95 % level.
02:40
And in order to do that, we are using the formula that says error bound of the mean equals t sub alpha over 2 multiplied by the standard deviation of the sample divided by the square root of n or the square root of the sample.
03:02
So because we are trying to find the 95 % confidence interval, we are going to put 0 .95 in the center of that bell shape curve.
03:12
The alpha in this case is the remaining part of the bell.
03:16
And if 95 % is accounted for, that means there's 0 .05 unaccounted for.
03:23
So we need to find the t value, the standard t value, associated with alpha over 2.
03:33
Alpha being 0 .025, alpha over 2 is going to be a 0 .025.
03:41
And that's referring to how much is in this left tail and the area that's in the right tail.
03:48
And in order to calculate this t value, we are going to have to use our graphing calculator, and we're going to access the inverse t function.
03:58
And when you use that function, it does ask you for the area of the curve.
04:04
It's in the left tail, so it's going to be 0 .025.
04:08
And it also asks you for the degrees of freedom.
04:12
And our degrees of freedom is always going to be n minus 1.
04:17
In this case, we were using 84 in our sample, so therefore our degrees of freedom is 83.
04:25
So i'm going to bring in the graph and calculator and show you where inverse t is.
04:31
So you're going to hit the second button, the distribution or variables button, and number four.
04:42
And it's going to ask you what is the probability or the area in the left tail, which is 0 .025, and it asks you for your degrees of freedom, and your degrees of freedom in this case was 83.
04:55
So therefore, our t value is negative 1 .989.
05:04
So what is that referring to? that negative 1 .989 is referring to the lower boundary of this confidence interval.
05:17
And because the t distribution is symmetric, then this upper bound is going to be positive 1 .989.
05:26
So in our formula, the error bound of a mean, we're going to use the 1 .989...