Activity 29

MATH 216: Statistical Thinking

Activity 1: Quiz

Q: When comparing two independent means, why do we add variances in the standard error formula?

a) Measurement errors accumulate
b) Variability from both groups contributes to uncertainty
c) It cancels out correlation between groups
d) The Central Limit Theorem requires it

Activity 2: Hands-On Distribution Explorer

Task: Simulate sampling distributions for two groups in R. Verify the standard error of the difference in means.

Activity 3: Environmental Science Application

Data: Air quality index measurements (Industrial vs. Residential zones)

Perform EDA with side-by-side boxplots
Conduct Welch’s t-test
Interpret practical significance

Activity 4: Education Policy Debate

Scenario: District A (new curriculum) vs District B (traditional). Test scores:

District A: n=200, \(\bar{x}\)=258, s=35
District B: n=180, \(\bar{x}\)=242, s=29

Compute 90% CI for difference
Formulate hypotheses
Calculate pooled variance t-statistic

Activity 5: Psychology Interaction Challenge

Data: Reaction times (milliseconds) for two cognitive tasks:

Task 1 | 320 | 298 | 310 | 285 | 305 |
Task 2 | 295 | 280 | 290 | 310 | 275 |

Perform paired t-test (same subjects)
Compare results with independent t-test approach
Discuss assumption violations