Confidence Intervals and Test Assumptions › Summary

This chapter covered two essential complementary topics:

Confidence Intervals and Their Equivalence to Hypothesis Tests

• A 95% CI contains all parameter values that would not be rejected at the 0.05 level
• CIs are more informative than p-values because they show the range of plausible values
• CI width communicates precision: narrow intervals indicate precise estimates

Test Assumptions

• Independence: The most important assumption. Violations lead to inflated Type I errors.
• Normality: The CLT makes this less critical for large samples (n > 30), but small samples require caution
• Equal variances: Use Welch's t-test as your default for two-sample comparisons

Choosing Between Tests

• Use t-tests when $\sigma$ is unknown (almost always)
• Use Welch's t-test as the default for two-sample comparisons
• The z-test is appropriate only when you know $\sigma$ from prior information