#Q67: Auto component quality

Let’s say you’re working to test product quality for an auto manufacturer, and you run a paired t-test with 700 observations covering the time to failure for a particular vehicle component.

The results of your test show that your company’s mean quality exceeds your closest competitor by 5 points, with a p-value of 0.02. How would you describe this outcome to a stakeholder? What does this p-value mean exactly?

Try it yourself

Answer

This question quickly tests our familiarity with interpreting statistical tests, in particular the T-Test.

Recall that a T-Test is a hypothesis test used to compare the means of two (& ONLY Two) groups or outcomes when the population variance is not known (Z-Test is preferred otherwise).

When describing the outcome to a stakeholder, be sure to emphasize that we have a large sample size at 700 observations and that the p-value is 0.02 meaning that the difference of 5 points is significant. The p-value is the probability of observing a difference at least as extreme as what was observed given the null hypothesis (there is no difference in the means) was true across multiple sampled observations.

In plain english, there is a 2 in 100 chance that we would observe something so extreme, therefore it is unlikely that this was due just to chance from our random sample.