Activity 24

MATH 216: Statistical Thinking

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 are the 8 steps in the systematic hypothesis testing framework? Briefly describe each step.
  1. How does the 8-step process ensure rigorous statistical evaluation of claims?
  1. What are common errors in hypothesis testing that the systematic framework helps avoid?

Part 2: 8-Step Process Application (4 minutes)

Apply the 8-step hypothesis testing process to real-world scenarios: Show your work for one complete 8-step process:

  1. Study Group Effectiveness: Claim that study sessions increase average test scores above 75
    • Sample: \(\bar{x} = 78\), \(s = 5\), \(n = 30\), \(\alpha = 0.05\)
    • Complete steps 1-8 for this scenario
  1. Nutrition Study: Claim that new diet reduces average calorie intake below 2200 calories/day
    • Sample: \(\bar{x} = 2150\), \(s = 120\), \(n = 35\), \(\alpha = 0.05\)
    • Complete steps 1-8 for this scenario

Part 3: Decision Framework and Interpretation (3 minutes)

Apply decision framework and interpret results:

  1. For the study group scenario (z = 3.29), what is the statistical conclusion? What practical implications does this have?
  1. For the nutrition study (z = -2.47), what is the statistical conclusion? How should this influence dietary recommendations?