0:00
All right.
00:02
So in this question, it's basically an intro to statistics question, which is dealing with distributions and sampling and sampling distributions and standard deviations and means and all that.
00:17
Right.
00:18
So let's take a look at first.
00:20
What we're given.
00:21
We're given is that the heights of men follow a distribution of 60, with the mean of 69 .3 inches.
00:30
So we'll use x bar m to denote that.
00:35
And there's also, they also have a standard deviation of 2 .8 inches.
00:44
But we'll come back to that part later.
00:47
It's not really that i'm putting out.
00:48
And the heights of young women follow distribution, normal distribution, with the mean of around 64 .5 inches, right? and they have a standard division of 2 .5 inches.
01:03
So the question asks, if they select an independent srs of 16 young men and nine young women, right? of 16 men and nine women and calculate the sample mean heights, which is x of m and x of w.
01:25
What would the shape of the sampling distribution actually look like? right.
01:32
So yeah, so let's just go ahead and start, right? so for the first part, that's the first part question.
01:43
So x bar sub m and x bar of w are the two normal, standard normal variants.
01:52
So this is just a thing in stats, right? so since these two are standard normal variants, right, then the difference of them, which is what they're asking us to do, they're asking us to take the difference of that.
02:06
So since these two are normal variants and the difference has to also be normal, right? so that means since in the question, right, they give us that heights of young men follow a normal distribution.
02:27
And women also follow a normal distribution, right? so since both of those follow a normal distribution, then stats basically tells us that the difference of those two normal distributions has to also be.
02:41
Normal.
02:42
So your answer down here would be the shape of x bar m minus x bar w is also normal.
02:56
And your reasoning is of course that since the parent variants are also standard normal, and this one has to also be standard normal.
03:07
Right? so let's move on to part b.
03:11
So here, let's see part b.
03:15
And part b, what they're asking us is to find the mean of the sampling distribution and show the work.
03:22
Right.
03:23
So the mean of the sampling distribution would be the mean of m minus the mean of women.
03:33
So then when we convert that, that would basically look like mu of men, and this is capital version minus mu of women...