00:01
All right, so a couple questions here based on the manager of a grocery store taking a random sample of 100 customers.
00:07
We find the average length of time was 3 .1 minutes with the standard deviation.
00:12
0 .5.
00:12
And the first thing when it was the degrees of freedom.
00:14
So the degrees of freedom is equal to the sample size and minus one.
00:22
The sample size in this case is 100 minus 1.
00:27
So that gives us 99 degrees of freedom for the first question.
00:34
Now, the second question wants us to determine the p value.
00:39
So in order to determine the p value, first we have to find the test statistic, which is a t score in this case.
00:44
The t score is in the box there, the formula from the t score, which is going to be the sample mean, which was 3 .1, minus the claimed population value of 3.
00:56
And we're going to divide that by the standard deviation .5 over the square root of 100.
01:07
And if we plug all this into the calculator, we get a t value of 2.
01:20
So the p value, if we were to set up hypothesis test, our alternative hypothesis would be that the mean is greater than 3.
01:34
So this is the same then as the probability t is greater than 2.
01:40
And we're talking about 99 degrees of freedom attached to that t.
01:45
So what we need to do is go to, in this case, we don't have 99 degrees of freedom because this table skips from 80 to 100.
01:54
So we'll just pick the 100 degrees of freedom value here on the left side.
01:59
And what i'm looking for is the closest to two that i can get or where two would fall between.
02:06
So if i go across the row here this way, notice that these numbers are going up and eventually i get to 1 .9.
02:15
Which is here, and then i jump over to and get to 2 .36, which is here.
02:22
And this will give us an approximation of rp value because it's not going to give us the exact number on this table.
02:30
So what we need to do is scroll up to the top.
02:33
And this is a one -tail test.
02:34
It's a right -tail.
02:35
This t -table gives areas in the right tail.
02:39
If you want it in the left tail, you just have to negate the values...