Activity 22
MATH 216: Statistical Thinking
Activity 1: Hypothesis Setup & Directionality
Scenario: Park benches allegedly fail before 5-year warranty (vendor claims μ ≥ 5 years).
Step 1: Frame Hypotheses
“Which claim becomes our default assumption (H₀)? Should our alternative hypothesis be left or right-tailed?”
Step 2: Direction Reasoning
“Why left-tailed?
Step 3: Error Contextualization
“Type I Error (\(\alpha=0.05\)):
Type II Error:
Activity 2: Test Statistic & Distribution Choice
Scenario: Sample data shows \(\bar{x}=4.2\) years, \(s=1.1\), \(n=35\)
Step 1: Distribution Selection
Z vs T:
Step 2: Standard Error Calculation
Step 3: t-Score Computation
Activity 3: Rejection Regions & Decision Making
Scenario: Critical t-value = -1.69 (\(df=34, \alpha=0.05\))