• Hypothesis testing is used to verify some claim about a population statistic, or hypothesis, based on some sample data.

1. To conduct a hypothesis test, start with a statistical hypothesis
2. Determine what the alternative hypothesis is, and an appropriate value for \(\alpha\) .
3. Perform the test or calculate the statistic on the sample dataset
4. Accept or reject the null hypothesis.

• A statistical hypothesis is a claim that can either be supported or rejected by some data.
• It is important to determine an appropriate hypothesis based on the situation
• Example
  • A statistician wants to test that the average time for a car to accelerate from 0-60mph is less than 8 seconds.
  • Null Hypothesis: \(H_{0} = \mu < 8\)
  • Alternative Hypothesis: \(H_{a} = \mu \geq 8\)

The value \(\alpha\) is what determines how strongly the evidence provided by the sample dataset must counterprove the null hypothesis before rejecting it. For example, when \(\alpha = 5\%\), there is a \(5\%\) chance that the tester rejects the null hypothesis when it is really true.