What are formal hypothesis tests?

A formal hypothesis test is like asking a question to see if something is true or not, and using a special kind of proof to answer it.

Imagine you have two types of candy: one that’s chocolate, and one that’s gummy. You think the chocolate candy might be more popular than the gummy one. So you ask your friends which they like better. That's like doing a hypothesis test, you’re checking if your guess is right.

In a formal hypothesis test, you start with two ideas:

• The null hypothesis (the "default" idea), like saying both candies are equally popular.
• The alternative hypothesis (your guess), like saying chocolate candy is more popular.

Then you collect data, maybe you ask 10 friends, and 7 say they prefer chocolate. You use this information to see if it's likely that chocolate is really more popular, or if it might just be a coincidence.

It’s like having a judge who looks at the evidence (your friends’ answers) and decides whether your guess should be accepted or not. That’s how formal hypothesis tests help us make smart guesses with real proof!