How to set up the null and alternative hypothesis

There’re things that are born to be rejected. Those include the null hypothesis and… everything my sister suggests ?. The first step to do in hypothesis testing is to set the null and alternative hypotheses, and as long as you remember the above sentence, you’ll know how to set up those hypotheses.

is always the fact that we want to reject. Here are a few examples:

Example 1 (blood sugar drug):

We want to test if a new kind of drug B is better at reducing blood sugar than the old drug A. We can test the hypothesis

where is the mean blood sugar for patients taking drug A and is the mean blood sugar for patients taking drug B.

Since we want to test if drug B is better at reducing blood sugar, we expect the mean blood sugar for patients taking drug B () to be smaller than the mean blood sugar for patients taking drug A (). Therefore the alternative hypothesis can be

Example 2 (GPA):

Suppose that I have an English center. I want to illustrate by statistical testing that the students who graduated from my competitor have lower IELTS scores than my center on average. Let be the mean score of the students who graduated

from my center and let be the mean score of the students who graduated from my competitor. Then the null hypothesis is

and since I want to show that my center is better, I would expect to be lower than . Hence my alternative hypothesis would be

Example 3 (Tire quality control):

I am to produce car tires and I claim that my product can last for 24 months. After buying tires from my company, many customers found that the tires lasted for up to 30 months (this is great, no complaints). However, many customers complained that the tires last only for 10 months. This is a big problem since it means that the variation in the product quality varies too much. So I need to find ways to reduce the variance of the tire lifetime. After some changes in production, I decided to test if the new production method reduces the variance of the tire lifetime. So suppose that the variance of the tire lifetime produced by the old method is and the variance of the tire lifetime produced by the new method is . Then I expect and therefore I would like to test

Versus

Conclusion

It sounds strange, but remember: You want to reject the null hypothesis and accept the alternative hypothesis. So we can say that we favor the alternative hypothesis more. This is completely opposite from the real world where an “alternative” means something that is less favored like “I love strawberries, but if strawberries get too expensive, then I can also get blueberries as an alternative.”