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.