1. Explain the logic of hypothesis testing: We assume the null hypothesis is true, then determine if our observed data would be surprising under that assumption.
2. Distinguish between a sample statistic and a test statistic:
- Sample statistic (x̄, p̂) = what we calculated directly from our data
- Test statistic (t, z) = standardized value used to compare to a reference distribution
- Explain why we standardize (to use established reference distributions and account for sample size/variability)
3. Explain that test statistics have sampling distributions (reference distributions like t-distribution, z-distribution) that we use to determine "how surprising" our result would be under the null hypothesis.
4. Interpret a p-value as the probability of observing a test statistic as extreme as (or more extreme than) what we observed, IF the null hypothesis were true.
5. Distinguish between the null hypothesis and the alternative hypothesis, and explain why rejecting the null does NOT prove the alternative is true.
6. Describe Type I error