📘 Chapter 9 Summary – Hypothesis Testing
This chapter introduced the logic and tools of hypothesis testing. You’ve learned how to evaluate evidence using sample data, test assumptions, and make decisions about population parameters.
✅ Key Concepts Covered
- Null & Alternative Hypotheses: Competing claims about a population (H₀ vs. H₁)
- Type I and II Errors: Rejecting a true H₀ (Type I), or failing to reject a false H₀ (Type II)
- Significance Level (α): Threshold for how much evidence is needed to reject H₀ (commonly 0.05)
- P-value: Probability of getting data as extreme as observed, if H₀ is true
- Critical Value Method: Compare test statistic to a rejection threshold (z or t)
- Confidence Intervals: Range of plausible values for μ, directly linked to two-sided tests
🧪 Z-Test vs. T-Test
- Z-Test: Use when population standard deviation (σ) is known
- T-Test: Use when σ is unknown and sample size is small (n < 30)
- Both test for the population mean and rely on assumptions of normality
🧠 What You Can Now Do
- Write and interpret hypotheses correctly
- Choose between one-sided or two-sided tests based on research question
- Compute and interpret p-values
- Conduct a one-sample z-test (σ known)
- Conduct a one-sample t-test (σ unknown)
- Connect confidence intervals and hypothesis testing conclusions
📌 What’s Next
- Tests for proportions (z-test for p)
- Variance tests (chi-square)
- Goodness-of-fit and independence (χ² tests)
- Nonparametric methods: Sign test, Wilcoxon test
- Combining p-values and small-sample strategies
🎯 Review this summary before moving to Chapter 10! Understanding this foundation will help you handle more complex testing situations later.