00:01
So in this question, we have already an example in item 1.
00:04
So we just need to replicate.
00:07
So here, let's start with the number 2.
00:14
So here, we first need to compute what is the t calculated.
00:19
So this here, because we are interested in the hsgpa, will have the same t calculated as item 1, because we are talking about the same thing, we are just changing the confidence level.
00:35
So the t calculator here is basically given by, in general, is given by the coefficient estimated for this, which is 412, divided by 0 .094, which is the standard error in parameter, inside the parentheses.
00:52
So this here will be the value that we have in item 1, 4 .38.
00:58
Now, the tick critical will be different because this tick critical here depends on the confidence level.
01:08
So if you're assuming that the confidence level now is 99%.
01:13
This means that i should find, so let me draw here.
01:18
This tick critical is in the right side of the distribution.
01:22
And because we're assuming a 99 % confidence interval, i will put here 99%.
01:27
Plus half of what is left when we subtract 99 % out of 100%.
01:36
So in this case is 1 % divided by 2.
01:41
So basically with this information, we need to use the t -sudence distribution with degrees of freedom equals 2.
01:49
In this case, we need to account for the number of parameters that we have in the model, so n times the number of parameters.
01:58
So we have the intercept, which is one parameter.
02:02
The slope for the hsgpa, so two, one parameter for the act, and one parameter for the sct, and one parameter for the skipped.
02:09
So we have like four parameters.
02:11
So we need to account for this, so n minus four.
02:14
So in our case, this is 21.
02:17
So now we can use the table to find this value.
02:20
So this value, he is 283.
02:23
So we're going to plug here to 883.
02:26
Now we need to compare the t calculated with the t critical.
02:31
So here what we should say is that the t that we calculated is greater than the t critical.
02:39
And because of this, the conclusion would be to reject the no hypothesis.
02:46
Okay.
02:47
Every time that our critical value is greater than our calculated value is greater than the critical we reject.
02:55
So now that we know how to do it.
02:58
Let's proceed for question three.
03:02
So now we are interested in the act.
03:06
So the t calculated here, using the same idea, is now the value of the slope for the act, divided by the standard error inside the parentheses.
03:18
So if you calculate this, what you're going to get is here, 1 .36.
03:27
Now, the t -critical here also depends on the simple size, right? so we're going to find the t -critical now.
03:39
I'm going to draw again.
03:40
So here the t -critical is this point in the t -student with, now that we have 200 observations, with 200 minus 4.
03:51
And the area left to it is equal to 97 .5%.
03:55
Using the same idea that we did in the previous item.
03:59
So here, if you use the t table, you're going to find now for this specific value of confidence, in the specific number of degrees of freedom, that the t critical is 1 .97.
04:16
So we're going to plug here.
04:19
Now, with this information, basically what we have here is that the t that we calculated is less, then the t critical.
04:28
So the conclusion is no.
04:31
Don't here reject the new hypothesis.
04:38
Don't reject the new.
04:42
Now for four, we can do the same thing, but now is for the 99%.
04:49
So the t that we calculated will be the same, so 136.
04:55
But now the t critical here will be different, because the area now is different, the 99 .5%.
05:04
So if you put 99 .5 % and use the table, you're going to find that this is 2 .60...