00:01
In this question in letter a, let's compute first the statistic for this test.
00:05
So here we are going to put the sample mean minus the value that we are testing, which is two liters, divided by sigma in the population, which is 0 .05, divided by the square root of the sample size, which is 100.
00:24
So this here is, if you compute this difference, you're going to find this value, which is negative.
00:31
Then we have this standard deviation in this.
00:36
These you're going to find minus 2.
00:38
In letter b, let's compute the p value.
00:42
So since this test is two -tail.
00:46
Why to -tail? because in letter a, they are saying that we are testing.
00:51
If the min amount in the bottles is different from two.
00:54
So we have this test.
00:56
We are testing if the mean is equal to two or it is different.
01:02
So as you can see, we don't have a direction here in the alternative.
01:06
So that's why there we have a two tail.
01:09
And because of this, the p value here is given by two times the probability in a standard number distribution of finding a value as extreme at this one, which is finding a value which is even more negative than that one.
01:28
And this here is, in this case, 0 .0455.
01:37
Now, if you make like an interpretation here, like i said, this here is the probability.
01:44
So this is the probability of finding a value, or in this case, a value for the statistic, which is even extreme than this one, more or as extreme than what we found.
02:12
And this is the explanation here...