- [Instructor] We're told a sociologist studying fertility
in Argentina and Bolivia wanted to test
if there was a difference in the average number
of babies women in each country have.
The sociologist obtained a random sample
of women from each country.
Here are the results of their test.
So they take a sample of 75 women in Argentina,
and these women had a mean of 2.4 babies each,
with a standard deviation of 1.5.
And then the standard error of the mean was 0.17.
And then they calculated similar statistics for Bolivia.
And then they give us the t test
for the means being different,
and we were able to calculate these statistics.
And they say assume that all conditions
for inference have been met.
At the alpha equals 0.05 level of significance,
is there sufficient evidence to conclude
that there is a difference in the average number
of babies women in each country have?
So pause this video, and see if you can answer that.
All right, now let's work through this together.
So this is classic hypothesis testing right over here,
where your null hypothesis is actually going to be
that your means are the same,
so that the mean in Argentina is equal
to the mean in Bolivia.
And then your alternative hypothesis is
that your means are different.
And what you do is you say, all right,
if we assume the null hypothesis, what is the probability
that we would have gotten means this far apart?
And that's what our p-value tells us,
that we have a 0.31 probability,
or a 31% probability, of getting means this far apart.
Now, if your probability, assuming the null hypothesis,
is below your level of significance,
your alpha right over here,
then you would say, all right,
that seems like such a low probability.
I'll reject the null hypothesis,
which suggests the alternative hypothesis.
But in this situation here,
if we compare our p to our alpha,
we see that our p-value is for sure greater than our alpha.
So in this situation,
I mean you could see it right over here,
0.31 is for sure greater than 0.05.
So in this situation, we cannot reject the null hypothesis,
cannot reject
our null hypothesis.
And so there is not sufficient evidence
to conclude that there is a difference
in the average number of babies women in each country have.