Welcome to Excel 2013 statistical analysis video
number 46.
Hey, if you want to download this workbook
and this is the second workbook for chapter 7,
click on the link below the video.
Hey, last couple of videos, chapter seven,
we've been talking about the sampling distribution of X bar.
And we saw if we actually had every single sample mean
possible, and we did this example in class where
we ran some VBA code to list all 6,000 plus possible samples,
then we got every single number for every single sample.
Then we came over here, and watch this.
Control-down arrow all the way down into the 6,000's.
Every one of these is one of the possible sample means.
Control-up arrow.
And then what did we do?
We plotted them.
And we noticed that if we plot actual X bars, which remember,
sample means are X bars.
Those are all measures of central tendency.
So if all these numbers tend to cluster in the middle
when you plot them, they're going to cluster in the middle,
and it looks like a bell distribution.
We also noticed that the pop mean equals
the sample mean of X bar.
We also talked about standard error.
But in this video, we want to actually look
at the standard error and see why the formula makes sense.
Now the reason we can do this is because we actually
have a list of every single sample X bar.
Remember this standard error is our formula to calculate it.
But what if we actually had all the values?
If we calculated the standard deviation,
it better be the same as this formula right here.
So let's come over to the side.
I have the X bars.
And guess what?
Even though these each individual item is a sample,
together this is a complete list.
So this is actually a population.
We also have our actual population x-values.
So what I want to do first is count the population size, then
the sample size.
Well, the population size count--
it'll just count numbers.
I'm going to count the actual numbers from the population
and enter.
Now our sample size, it was giving us 5,
but I'm still going to do a formula.
I'm going to count.
Look at this.
If I scroll over here, every single sample had how many?
One, two, three, four, five.
Tab, that counts five.
Now one thing about our original sample and our sample size
is that when we do our formula over here for standard error,
normally, we don't have to do this correction factor,
but here, we are.
Now let's calculate the standard deviation from our population.
STDEV.P, simply highlight the original population numbers,
and enter.
So we get 31,000 about is our original standard deviation.
Now let's calculate sigma of our expected x bar, which
is the means of all the means.
And here's the thing.
It's a population, so we use the P. Scroll over here,
Control-Shift-Down Arrow.
Shift-Enter to enter that in the cell and have the cell jump up.
So there it is.
Actually, because we have the full list,
we can just calculate sigma of expected X bar right there.
But let's do our formula now, equals--
and this is the formula we were given.
We have to take population sigma because in this chapter,
and in some cases, you have it, so you
need to be able to derive the standard deviation
from the sampling distribution of X bar given that you have
population standard deviation--
our population size and our end size.
So we take sigma divided by the square root
of our N. That's our 5.
And I'm going to enter this right now.
That would be if we had an infinite population
or the division of this was greater than 5%.
Let's just do our calculation over here
and say sample size, n, divided by big N. And this is 29.
If you remember our rule for when
to use the correction factors when this was greater than 5%,
so this is gigantic.
So we have to use our correction factor.
So here it is--
times square root in parentheses big N minus little n close
parentheses.
That's in the numerator divided by in the denominator big N 17
minus close parentheses.
Close parentheses on the square root.
And when I enter, it exactly equals.
So we're doing this because we have our complete list
over here of all of our sample means,
so we can calculate it directly.
But we just wanted to see that when
we're given population sigma, big N a little n,
and we calculate this using this formula here,
it'll give us exactly the right number.
Last video for chapter 7 will be in the next video.
And we'll look at one last example
of how to use the central limit theorem.
See you next video.