Conclusion for a two sample t test using a P value

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. Then the standard error of the mean was 0.17. Then they calculated similar statistics for Bolivia.

Then they give us the t-test for the means being different. 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. 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? That's what our p-value tells us. We have a 0.31 probability, or 31 percent 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.