Welcome to Excel 2013 Statistical Analysis Video
Number 61.
Hey, if you want to download this workbook,
Business 210, chapter 9, second file, click on the link
below the video.
And this is our last video for chapter 9.
We going to do hypothesis testing for proportion.
Here's our question.
The school newspaper stated that the proportion of students
who knew when the presidential election would be held was 15%.
A researcher thought that this was low
and wanted to show that the proportion of students
who knew when the presidential election would be held
is higher than 15%.
The researcher took a random sample
and made sure he got respondents from all
of the different demographics, including
night students, online students, new immigrants, and others.
At alpha, 0.01, can the researcher
conclude that more than 15% of the students
know when the presidential election will be held?
Now one thing the researcher probably did
is they thought, well, this seems really low.
Maybe they made an error when they sampled.
The population being sampled maybe
didn't include some of the group.
So when the researcher went out, they
made sure to try and get all of the different--
do a true random sample that really
sampled the actual population at this school.
Now the thing about proportions is
we've got to check if it's binomial.
And we've done all of the calculations
we're going to do here in earlier chapters
when we did proportions.
We have to check whether or not this is a binomial test.
Is there a fixed number of trials yes? .
We'll see there's exactly, we asked 152 students.
Probability stays the same each time?
Yes.
Yes or no.
Trials are independent?
We'll assume that they are.
Each trial results in a success or not?
A success.
Yes.
Well, what is a success going to be for us?
It's going to be answering yes, I do know.
Not success will be they don't know.
All right.
And so we have these four tests, but then there's five, six.
We have to make sure that n times P is
greater than or equal to 5 and n times 1 minus P.
So I went ahead and already calculated these.
And in both cases they were greater than 5.
Here's our hypothesized population proportion--
0.15.
Now before we set up our test--
let me scroll down here--
we got to look at the point of view and the goal.
The point of view is a researcher
who is skeptical of the reported proportion
of the number of students who knew when
the presidential election was.
So that's our point of view.
Our goal-- test to see if there are significantly more than 15%
of the students who knew when the presidential election would
be held.
So we're looking-- again, significance.
That means we have to pass that hurdle before we
reject the null and accept the alternative.
The more than 15%, that phrasing or that thinking
of what we're doing here, helps us setup the null
and alternative hypothesis.
So I'm going to come right down to the alternative,
because this more.
Notice we do our little symbol, right?
That means it's pointing.
That little small side is pointing
towards the upper or right side so this
is a test on the upper side.
So I'm immediately going to come here.
We do the same thing, except for instead of mu,
we use P. So is the proportion greater than 15%?
Now remember once we know the alternate,
we go up to the null hypothesis and flip it.
Less than or equal to.
The equal sign always goes with the null hypothesis.
All right.
Alpha is going to be 0.01.
We want to be super sure here.
We want to set the hurdle high.
Remember if the alpha is low, then the hurdle is high.
Type I error is reduced when we increase alpha,
which means we have less of a chance of rejecting
the null hypothesis even though it was true.
All right.
Now we need to come up and make some calculations
from our sample.
OK, so we have a sample, yes or no, knew when the election was.
I'm going to count the yes's and the no's.
So yes, we're going to use the function count if.
Count not everything, but count if some condition is met.
So the range.
I'm going to click in that top cell.
Control-Shift-Down Arrow and F4 to lock it.
Comma.
And I've set up my criteria yes and then no
on top of each other.
So I'm going to click there as a relative [? SAR ?] reference.
Control-Enter, and then when I copy it down,
we got the right now.
So we have 36 and 116.
Now this is our total and now we can calculate our probability.
By the way, this should look familiar.
This is what we did in chapter 2 when we did relative frequency.
So I'm going to say the part divided by the whole.
F4 on the 152.
So we have a probability yes of about 2.4 and about 0.76.
All right.
Now we can go ahead, and here's our sample proportion.
Our Pbar.
So we come down here.
We have step 1, step 2, step 3.
We have our 0.2368.
That'll be our Pbar.
We have to calculate our standard error.
And the formula is page 28 in the PDFs,
but here it is right here.
We've done this in earlier chapters.
Square root.
And we're going to take our--
actually, we want to go up and get it
from our source, our place right here.
So it's P times 1 minus, and then divide by n.
And the order of operations will work fine there.
They're all left to right, so close parentheses.
And our standard error is going to be 0.0289.
Now we can calculate our test statistic, right?
Whatever our statistic is minus the hypothesized parameter
divided by the standard error.
So we say in parentheses, and it's down just a little bit.
There's our Pbar minus our hypothesized proportion
up there.
Close parentheses, divided by our standard error.
Wow so we've got 2.9.
Now the distribution we use for proportion
is the z distribution.
So that's 2.9.
Almost 3 standard deviations above.
You can already guess.
I mean, this is the seventh or eighth test
we've done in this chapter.
That's way above.
3 standard deviations above.
So we're probably rejecting the null
and accepting the alternative.
Let's go ahead and calculate our P value.
Now if we calculate a P from this, this is on the upper end
and we want the probability above it
so we have to do 1 minus.
And back to our norm dot.
So I need my S for the standardized normal
distribution.
So there I have my Z. Comma 1 cumulative.
It'll calculate all the way up to this, which is a lot,
and then 1 minus that will give us our probability.
So this value here is amazingly small,
which means it gives us very strong evidence
that we should reject the null and accept the alternative.
We compare it directly up to here,
and obviously much smaller.
Our critical value rule, we're going to use the inverse.
So norm dot S dot inverse.
And our probability-- well, we're on the upper end,
so we need to say 1 minus r alpha.
Our critical value is 2.32.
So comparing that, anytime our test statistic
is greater than or equal to this, we reject the null
and accept the alternative.
So either way you go, we come to the same conclusion
as we said many times so far.
Our conclusion-- because the P of approximately 0.0014
is less than or equal to our alpha, we reject the null
and accept the alternative.
If we're using our critical value rule because the test
statistic 2.99 almost-- it's 3 standard deviations,
in essence--
is greater than or equal the critical value of 2.33,
we reject the null and accept the alternative.
There is strong statistical evidence
to support the claim that more than 15% of the students
know when the presidential election will be held.
Said a different way, that alpha of 0.01,
our sample proportion of about 0.24,
provides very strong statistical evidence
to suggest that more than 15% of the students
know when the presidential election will be held.
And finally, we do run a 1% type I error
risk of saying that more than 15% of the students
know when the election will be when in fact they do not know.
Now again, once you get a P-value like this,
this is very strong evidence.
All right.
That's hypothesis testing for a proportion.
We've done a lot in chapter 9.
We'll see you next video.