Welcome to Excel 2013 Statistical Analysis, video
number 56, and if you want to download this workbook,
Business 210 Chapter 9 second workbook, click on the link
below the video.
Hey, in the last three videos, we
did hypothesis testing, all three examples-- one tail
right, one tail left, and two tail when sigma is known.
This video is just a quick summary,
so you have all of the formulas and functions in one summary
video.
All right, one tail to the right upper test--
that means we're testing on the upper end.
We have all of our data here.
We have to calculate standard error before we
can do the test statistic.
Standard error is always going to be, when sigma is known,
sigma divided by square root over n.
That gives us the standard deviation for the sampling
distribution of x-bar, which is going to be--
almost going to have less variation than the population
distribution.
All right, so we have that.
Now, we can calculate our test statistic.
We want to do, in the numerator, the sampling error.
There is our x-bar minus our hypothesized mean,
and we divide it by the standard deviation
for sampling distribution of x-bar, which is standard error.
So there we have it.
I'm going to Control-Shift-Tilde.
That is z.
That's our test statistic.
It tells us, for our sample mean,
how many standard deviations above or below.
So this one's above, so we're testing--
our original hypothesis was, we thought
that the mean salary for realtors
was greater than $85,000.
We get a sample.
Here's the number of standard deviations
above the assumed mu.
Now, we can calculate p value.
Now, when we calculate p value, we
compare it directly to alpha.
If p value is less than alpha, then we
reject the null hypothesis.
So for p value, we use equals, and these are the norm.s.
These are the standardized normal bell
shaped distributions, and we're going to use the DIST
to go from a z comma 1--
going from a z to a probability.
Now, that's from negative infinity up to our z,
and that's not what we want, so we have to take 1 minus.
That gives us our p value.
And what's the meaning of p value?
It means this test statistic--
what's the probability of getting
that test statistic or more?
So there, you can see the picture.
There's the probability.
That probability right there is smaller than our alpha,
so we would reject the null hypothesis
and accept the alternative.
Now, for the critical value method,
we have to take our alpha.
And I want to use our standardized normal bell shaped
distribution functions, but we're going to use the inverse.
The inverse, we take our alpha, and this
will deliver a z, which is our marking point, our hurdle.
Same thing-- we gave it 0.05.
That doesn't work because these functions always
go from negative infinity up to our point,
so instead of putting 0.5 in, we want 1 minus.
That gives us 95%.
So [MAKES FUNNY NOISE] up to there, that'll give us above.
So it's 1.64 for critical value.
That's the hurdle point right there.
So if our test statistic is above,
then we reject the null hypothesis
and accept the alternative.
That's one tail right on the upper.
One tail left on the lower--
we have 16 ounces of ketchup, and we
have a Control-Shift-Tilde to get rid
of that formatting, which means we did a sample
and got bottles of ketchup less than the hypothesized mean.
This is a test on the left, the lower end.
We have to calculate our standard error.
We're going to take our sigma divided
by the square root of our n.
Then we calculate our test statistic.
We need our sampling error in the numerator
divided by the standard deviation minus 0.8.
Our p value-- we are from negative infinity
up to that point, so no problem.
We can just throw in our z here, so we do norm.s DIST.
There is our z comma 1.
The 1 says calculate the cumulative probability
from negative infinity up to our z.
So there it is--
0.21.
We compare it directly to our alpha.
Much, much, much bigger, so we fail to reject.
Hey, here's something odd that happened.
Right there, you can't see all that,
but if you scroll up and then back down,
it magically appears.
I wish they'd fix that.
All right, critical value--
again, we have to--
here's our critical value.
That's the hurdle point.
Anything below for a lower left test,
any test statistic below, then we reject.
We'll use our standard normal curves, our s's.
Inverse goes from a probability to a z.
We're going to throw in our alpha, which then will spit out
our hurdle point.
Now, notice negative infinity up to that,
so we just leave it 0.05.
So that's minus 1.64.
We can clearly see that our test statistic is not
less than this, so we fail to reject.
Our last example is two tail.
Here's our little picture.
This one's not so symmetric here.
This is 16 ounces of ketchup, but the manufacturer
wants to check if the filling machine is out of balance.
We got a sample of 16.12.
We still have to calculate our standard error, our test
statistic, particular x-bar minus the hypothesized mu.
That is our sampling error, and we divide it
by the standard deviation to get how many standard
deviations above or below.
Now, we use our test statistic, either in the p value method
or critical value method.
Now, for p value, if we take this 1.444,
we know that p value gives us the probability
of getting 1.44 or more.
It's a two tail, so we're going to have
to take that probability and double it.
All right, you ready?
Equals-- and this is on the upper end,
so if we put in our 1.44, it'll give us
the probability from here all the way up to that.
So we need to 1 minus norm.s DIST.
We have our z comma 1.
Now, this will give us the probability on the upper end,
but we need to double it.
So I'm going to put parentheses around this
and multiply it by 2.
Now, down here, I have notes for all the different types
of tests--
the two one tails and the two tail.
This'll be p value up here.
So another way to do this--
norm.s DIST, and I'm going to take the opposite.
So this is on the upper end.
Now, this is going to force it to be on the lower end.
And so that gives us the same probability,
and we simply multiply it by 2.
And so for the critical value, we're going to use our norm.s
inverse, but we're given an alpha-- watt-- of point--
let's see-- 0.05.
We're interested in dividing that in half on either end,
so when we do our equals norm.s inverse,
we have to take the probability and divide it by 2.
Now, this'll give us our prob-- our critical value
on the low end, our hurdle, and so to get it on the upper end,
I'm just going to say minus this.
And notice, I didn't type in equals sign Control-Enter.
You type that minus.
It'll automatically put the equal sign in.
And then you can clearly see our test statistic, 1.44, is
between these two, so we fail to reject the null hypothesis.
All right, so that's a summary.
Six examples-- a p value and a critical value
test statistic calculation for each one of our tail tests.
All right, now, coming up in the next few videos,
we'll be talking about what to do if we don't have sigma,
our standard deviation for the population,
and we'll see how to use the t functions.
All right, see you next video.