00:01
Hey there, welcome to numerate.
00:03
We are given a problem here looking at the sample of 50 with our mean and population standard deviation given.
00:11
So with that, we will write our no and alternative hypothesis down.
00:16
So h -n -no and h -a.
00:22
So for h -node, we have mu that is greater than equal to 20.
00:29
We also have mu that is less than 20.
00:35
So now with this, this is our null and alternate hypothesis.
00:41
We can safely assume that this will be a left tail test.
00:45
Since we are looking at for alternative hypothesis, mule was less than 20.
00:52
So let us write the test stat.
00:56
Test stat will use a z distribution test.
01:00
So it will be z equals.
01:02
So the reason why we're using a z distribution test is because we are given a population standard deviation.
01:10
So x, x bar, it will be our sample means.
01:15
So our sample mean is 19 .1 minus our hypothetical mean, which is 20, divided by our standard deviation.
01:25
Standard deviation is 2 divided by the square root of our sample size.
01:31
In this case, our sample size is 50.
01:39
All right, so let's solve for our z score.
01:43
We punch you in a calculator, and we should get a z score of around negative 3 .1.
01:47
8.
01:52
All right...