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## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 11

Lesson 5: Testing for the difference of two population means

# Conclusion for a two-sample t test using a P-value

Given results of a two-sample t test, compare the P-value to the significance level to make a conclusion in context about the difference between two means.

## Video transcript

- [Instructor] A sociologist studying fertility in France and Switzerland 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 you can see a 100-person sample from France, a 100-person sample from Switzerland. They actually don't have to be the same sample size. We have our sample means, our sample standard deviations. You have the standard error of the mean, which for each sample would be our estimate of the standard deviation of the sampling distribution of the sample mean. And here it says t test for the means of these different populations being different. And just to make sure we can make sense of this, let's just remind ourselves what's going on. The null hypothesis is that there's no difference in the mean number of babies that women in France have versus the mean number of babies that women in Switzerland have. That would be our null hypothesis, the no news here hypothesis. And our alternative would be that they are different. And that's what we have right over here. It's a t test to see if we have evidence that would suggest our alternative hypothesis. And so what we do is we assume the null hypothesis. From that you're able to calculate a t-statistic, and then from that t-statistic and the degrees of freedom, you are able to calculate a p-value. And if that p-value is below your significance level, then you'd say hey this was pretty unlikely scenario, let me reject the null hypothesis, which would suggest the alternative. But if your p-value is greater than your significance level, then you would fail to reject your null hypothesis, and so you would not have sufficient evidence to conclude the alternative. So what's going on over here? You really just have to compare this value to this value. It says at the alpha is equal to 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? Well we can see that our p-value, 0.13, is greater than our alpha value, 0.05. And so because of that, we fail to reject our null hypothesis. And to answer their question, no there is not sufficient evidence to conclude that there is a difference. There's not sufficient evidence to reject the null hypothesis and suggest the alternative.