Activity 23

MATH 216: Statistical Thinking

P-Values and Hypothesis Testing Evidence

Time Allocation: 15 minutes total (5 min reading, 10 min individual work)

Part 1: Conceptual Understanding (3 minutes)

Instructions: Answer the following questions based on the lecture content:

  1. What is the correct definition of a p-value? What does it measure in hypothesis testing?
  1. Explain the difference between P-value calculation methods for right-tailed, left-tailed, and two-tailed tests.
  1. What are common misinterpretations of p-values that we should avoid?

Part 2: Real-World P-Value Applications (4 minutes)

Calculate and interpret p-values for real-world scenarios:

  1. Medical Research: Clinical trial shows z = 2.3 for treatment effectiveness (two-tailed test) P-value = Interpretation:

  2. Quality Control: Process improvement shows z = -2.8 for defect rate reduction (left-tailed test) P-value = Interpretation:

  3. Market Research: Consumer preference change shows z = 2.1 (two-tailed test) P-value = Interpretation:

Show your work for one calculation:

Part 3: Evidence Strength and Decision Making (3 minutes)

Evaluate evidence strength and make decisions:

  1. For the medical research case (p = 0.0214), what is the strength of evidence against H₀? Should we reject H₀ at α = 0.05?
  1. For the quality control case (p = 0.0026), what is the strength of evidence? What practical decision should management make?

Critical Thinking: Why is it important to distinguish between statistical significance and practical significance?