00:01
Here we have six questions about hypothesis tests.
00:03
Let's start with question one.
00:05
So we're looking at a two -tailed test.
00:07
Let me draw a sampling distribution here.
00:10
And we want to know when we would retain the null hypothesis.
00:14
So the level of significance is 0 .05.
00:18
I put that as alpha.
00:20
And since it is two -tailed, there are two rejection regions.
00:25
One down here, one up here.
00:27
The critical value we've been given is 1 .96.
00:31
And since there are two rejection regions, you would reject the null hypothesis if your statistic is down here or up here.
00:39
You would retain it if it falls in this area.
00:42
So between minus 1 .96 and 1 .96.
00:46
The only thing you need to know is, is it inclusive? it is.
00:49
It is inclusive.
00:51
We only reject if it is less than the critical value.
00:54
If it's equal to, we fail to reject.
00:59
Part two.
01:01
Now we might make an incorrect decision.
01:04
How can you increase the probability of making a correct one? so a is great if you decrease probability of committing a type two error.
01:12
Let me draw another curve here to represent this.
01:16
So this represents the actual distribution.
01:20
This one is assuming the null hypothesis is true.
01:22
This is the actual.
01:24
If your test statistic falls into this bit here, then you would fail to reject the null hypothesis, even though the mean is obviously different.
01:35
That would be a type two error.
01:38
So it's a false negative.
01:42
Now we could decrease the probability of that happening by increasing the sample size.
01:47
So we're actually going for option c.
01:49
So a is great, but the way of doing that is to increase the sample size.
01:54
Generally a very good thing in any kind of testing or confidence intervals.
01:59
Three.
02:00
As sample size increases, so i mentioned it decreases the type two error, it's because it makes both of these narrower, which gives us a smaller proportion that is in this error region, because they're further apart.
02:16
Put them back together...