00:01
The question wants us to find the critical values or the z values for each of the five examples that they gave.
00:09
For part a, they gave us an alpha value of 0 .02 and asked us for a left -tailed test.
00:18
When we draw out the picture of what that would look like, our left tail is going to be the area under the graph right here, and we are looking for this critical value here.
00:31
So the alpha of 0 .02 tells us that the area under here is 0 .02.
00:41
And when we look up the chart in table e, it will tell us the area to the left of the critical value.
00:48
So when we look up the chart, it'll look something like this in the middle here.
00:54
And since our left -tail test is on the left of the critical value, we're looking for 0 .02 in the chart.
01:03
The chart gives four decimal places, so i would recommend going ahead and writing out the four decimal places, just so you don't confuse yourself.
01:15
And we will find .02 at negative 2 .55.
01:24
So i only wrote the positive values here, but the negative values are in the first half of the chart, and the positive values are in the second half.
01:32
So in the first half of the chart, which will look almost identical to this other than the negative values, you'll find 2 .5 around here somewhere.
01:43
And these represent the whole number and the first digit after the decimal.
01:50
And then up here on the other axis, you've got the second decimal place, which will be a 5.
01:59
So you'll find that under the .05 column.
02:04
So where these two meet creates the z value of 2 .55, and you'll see that that will give you 0 .0202, and that is as close to 0 .02 as we can get on the chart.
02:26
That means that, sorry, this will be a negative value here and a negative value here.
02:32
So our answer for part a will be negative 2 .55, or you could say z equals negative 2 .55.
02:46
All right, so i will erase this and move on to part b.
02:51
For part b, they want an alpha value of 0 .05, and they want a right -tailed test.
02:59
And this answer was actually shared with the previous question in the test.
03:05
Textbook.
03:08
So i'll go ahead and draw out what that looks like.
03:14
So we'll have a bell curve.
03:18
This time the tail is on the right.
03:22
And this area is 0 .05.
03:29
Since the chart only tells us the area to the left of the critical value, we will want to subtract that from one to figure out that this area over here is 0 .95, or you can think of it as 95%.
03:47
This means that we'll be looking for 0 .95 in the chart, and you can fill that with zeros to four decimal places.
03:59
And this one will actually be exactly halfway in between two values in the chart.
04:06
There is, let's see, 1 .64.
04:10
So there will be a 1 .6 around here, and that will match with .04, and that will give you 0 .945.
04:28
And then the next value over, which will be at 0 .05, will give you 0 .9505.
04:42
So once again, 0 .95 is exactly halfway in between.
04:46
So we would take the value that is halfway in between 1 .64 and 1 .65.
04:54
And that would be 1 .645.
04:59
This would be the answer.
05:01
However, i usually go ahead and just round that number up to be 1 .65.
05:14
Either answer would be considered correct.
05:18
Keep in mind that anytime you have a right tail, it'll be a positive answer.
05:24
Anytime you have a left tail, it'll be a negative answer.
05:27
If you were to have a two -tailed test, which we will have for the next one, you'll want to include both the positive and the negative answer.
05:36
So for the next one, for part c, we will have an alpha of 0 .01, and it is a two -tailed test.
05:52
So erase all this real quick for that...