Hypothesis Testing - One-Sided Confidence Intervals (Upper & Lower Bound): Z-Test vs. T-Test Examples

The two-sided confidence interval is a staple of statistics, but sometimes your question only cares about one direction! In this video, we deep-dive into one-sided confidence intervals—the crucial statistical tool used when you only fear error on one side (e.g., is the mean too high or too low?). We explain the connection between the confidence interval and a one-tailed hypothesis test, demonstrating how to properly find the critical value (Z or t) and interpret the results. We work through two full examples: 1. Upper Bound Example: A Z-test scenario where we test if a mean is too low. 2. Lower Bound Example: A t-test scenario (small sample size) where we test if a mean is too high. This video is essential for students in AP Statistics, College Statistics, and anyone involved in Quality Control or Research where single-direction protection is needed. Video Timestamps (Table of Contents): 0:00 - Introduction: Why Bother with One-Sided Intervals? 0:31 - Two-Sided vs. One-Sided Recap (When to use each) 1:44 - Example 1: Upper Bound (Z-Test) 2:39 - Standard Error (SE), Critical Z, and Upper Bound 3:01 - Interpreting the Upper Bound Result (Rejecting a Claim) 3:31 - Example 2: Lower Bound (T-Test) 4:25 - Finding Critical t Value with Degrees of Freedom 4:43 - Calculating Standard Error and Lower Bound 5:02 - Interpreting the Lower Bound Result (Retaining the Claim)