Activity 23 – Math 216: Statistical Thinking

Activity 1: Think-Pair-Share

Prompt: Reflect on the role of \(p\)-values in hypothesis testing.

Think: Define the \(p\)-value in your own words.
Pair: Compare definitions with a partner. Discuss:
- Is the \(p\)-value the probability that \(H_0\) is true?
- How does it guide decisions about \(H_0\)?
Share: Present key insights (e.g., “\(p\)-value quantifies evidence against \(H_0\)”).

Activity 2: Quiz

Question: For a right-tailed test with \(z = 2.33\), find the \(p\)-value.

Activity 3: Data Exploration

Dataset: Breaking strength of pipes (\(n=50\), \(\bar{x}=2460\), \(s=200\)).
Task: Test \(H_0: \mu \leq 2400\) vs. \(H_a: \mu > 2400\).

Activity 4: Full Hypothesis Test

Scenario: Test if a pipe supplier meets \(\mu = 2450\) psi (sample: \(n=50\), \(\bar{x}=2420\), \(\sigma=210\)).

Activity 5: z-test vs. t-test (Critical Thinking)

Objective: Compare z and t tests for small vs. large samples.

Prompt: Given a sample (\(n=15\), \(\bar{x}=105\), \(s=10\)), test \(H_0: \mu = 100\) vs. \(H_a: \mu > 100\) using both tests.

Activity 6: Two-Tailed Test Interpretation

Objective: Practice calculating and interpreting two-tailed \(p\)-values.

Prompt: A study claims the mean reaction time is 250 ms. Your sample (\(n=40\), \(\bar{x}=255\), \(s=30\)) suggests otherwise. Test \(H_a: \mu \neq 250\).

Questions:

Why double the one-tailed \(p\)-value?
Interpret the result: Should we reject \(H_0\) at \(\alpha = 0.05\)?