Conclusion for a two-sample t test using a P-value
About this video
A sociologist compares the average number of babies women have in France and Switzerland using a two-sample t test. The video reviews the null and alternative hypotheses, explains how a t-statistic and degrees of freedom give a P-value, and compares the P-value of 0.13 to a significance level of 0.05 to conclude that there is not sufficient evidence of a difference.
You'll be able to
- state the null and alternative hypotheses for a two-sample t test for a difference in means.
- compare a P-value to a significance level to decide whether to reject the null hypothesis.
- write a conclusion in context when we fail to reject the null hypothesis.
Key words
- Null hypothesis
- The 'no news' claim that there is no difference between the population means.
- Alternative hypothesis
- The claim we look for evidence of; here, that the two population means are different.
- P-value
- The probability of getting a result at least as extreme as ours if the null hypothesis were true.
- Significance level (alpha)
- The cut-off, such as 0.05, that the P-value is compared against.
- Fail to reject
- The decision when the P-value is greater than alpha: the data do not give enough evidence against the null.
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.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.