00:01
Here we are asked, with a significance level of alpha equals 0 .05, the two -tailed critical region for a t test using a sample of 20 participants would have what boundaries? now since it's a two -tailed test, that means there are two critical values.
00:21
So we have one on the positive side of the distribution and one on the negative side of the distribution.
00:28
It's a t test, which means it's based on the t distribution.
00:30
And if it's based on a t distribution, we must have some degrees of freedom.
00:37
For this t test, the degrees of freedom is n minus 1 or 19.
00:43
And because it's two -tailed, that means each of the tails beyond the critical values is going to have alpha over 2, an area of alpha over 2 in each tail.
00:56
So we can denote this t sub alpha over 2, comma, 19 degrees of freedom.
01:02
And graphically, if this is the t distribution with 19 degrees of freedom, there's two critical values, one on the positive side, one on the negative side, such that the area in the tail is beyond them is alpha over 2, which in this example is .025.
01:49
So we can write this as plus or minus t sub .025, 19 degrees of freedom.
02:00
And so let's first solve this one.
02:02
So the probability that t distribution is less than this critical value, let's call it t sub -cr, is 0 .025.
02:20
Now let's use excel to solve this, and let's not forget this is negative, the negative of the critical value.
02:30
So in excel, we can type equals to start a computation...