In this chapter
- Intuition behind hypothesis testing and p-values
- Hypothesis testing for means, using two-tailed and one-tailed tests
- p-values and how to interpret them
- How to approach smaller samples and proportions with hypothesis testing
A hypothesis is a premise or claim we want to test, such as “Does my 305 mL can of soda really contain about 305 mL?” Just because the can advertises 305 mL (the null hypothesis, or the “status quo” claim) doesn’t mean that it is true. The competing claim, that the can does not contain about 305 mL, is called the alternative hypothesis. No can is going to have exactly 305 mL, of course, but we expect it to be close enough to that amount for the advertised claim to be valid. If it is not, perhaps the soda factory equipment changed, or maybe the company is erring on the side of being over (or under) 305 mL.
Hypothesis testing is a statistical experiment we conduct to test a claim. In the case of our can of soda, we are testing the claim that it contains 305 mL, as advertised. But to do that, we need to take a sizable sample (textbooks say more than 30 cans, or use the t-distribution if the sample is smaller). Then we measure the sample mean and standard deviation and show that the sample is not just different, but very different, from the claims about the population. Only then can we give credibility to challenging the claim.
