00:01
So let's take a look at what is given here.
00:03
So we have the 80 and the alternative hypothesis.
00:06
We have to just make this setup here.
00:10
So first of all, let's try to note what is given here.
00:14
So it says the moon value, the mu, which is 48.
00:20
And there's a 21 back sample.
00:23
So the sample size, which is denoted by end.
00:26
This is 21 here.
00:29
And the next one, the mean value, is 400.
00:33
So this is a sample mean.
00:34
So i can just write this is x bar, which is given as 451.
00:38
And also the variance is given here.
00:41
So the variance, which is given as 625.
00:46
If i want to get the standard division of the sample here, the standard division, standard deviation, which is equal to square root of the variance, so this is equal to the square root of 625, that would be 25 here.
01:02
So that means the sample standard division, which is denoted by s, this is 25.
01:08
And also there is given the evidence level here, which is 0 .05.
01:12
So the alpha is equal to 0 .05 here.
01:15
So what is supposed to be here? so when we look at the given data here, the population standard division is not given.
01:22
So the population standard deviation is not given or not known.
01:30
So what am i supposed to? i'm going to use the t test here.
01:35
First of all, let's set up the alternative hypothesis.
01:39
It says, is there sufficient evidence that the 0 .0 5 level that the backs are overfilled? so that means the alternative hypothesis is to say the mue value is overfilled means this is greater than 448.
02:00
And 48 and the null hypothesis just said this is mu is less than or equal to this is 448 first of all let's get the t score here so i'm going to get the t score the t critical value which is equal to so i'm going to just subtract the mean value so this is the mu minus the x bar i'm sorry this is x bar minus the moon value divided by standard deviation and divide by by the by the by squared of the sample size here let's get the value the x bar here is 451 minus the mean value is 448 divided by the sample standard division which is 25 and divided by the sample size the sample size was given as 21 which is this value let's get the value here this is 3 divided by i'm going to put the parentheses this is 25 divided by squared of 21 so it is 0 .54 and 991.
03:09
So this is the t critical value here.
03:12
So what we're supposed to do here? first of all, let me just draw the shape here.
03:18
So we have a normal distribution.
03:20
And the t value here is 0.
03:22
This value here, let's say this is the t value, 0 .54 -991.
03:29
And we're looking for the greatest one.
03:31
So we have to just find the area of this region here.
03:36
So for the area of this region, which is denoted by this is the p value.
03:40
So it is the x bar value, which is greater than 0 .54 .991.
03:49
So what i'm going to do here, i'm going to use the t distribution here...