00:01
So to understand what we're discussing here, i'll sketch out two distributions.
00:07
So we have our null -hypothesized distribution, centered at that null -hypothesized value, and then let's say that we have our actual distribution.
00:19
Actually, let me move it over a little bit so i can illustrate this a little bit more easily.
00:23
Let's say that the cutoff, critical value for our test, is right there.
00:32
So the area in red would be our alpha, our level of significance.
00:41
But we can see that under the actual distribution, where we can see, okay, well, this is the true value of the mean, it's not equal to the null hypothesized value, everything to the left of that critical value would be this region where if the null hypothesis is false, and it's actually, our distribution is actually following this blue distribution here, it's still possible that we might get the result where we fail to reject the null hypothesis.
01:13
We don't get something far enough away from the null hypothesized mean to have significant evidence against it, even though the null hypothesis is false.
01:22
So this would be a case of a false negative.
01:27
We fail to reject the null hypothesis when it's actually false...