Hypothesis Testing and the Flint Water Crisis

Nov 4, 2024

In-Class Activity 11a: Introduction to Hypothesis Testing

Overview

  • Introduction to hypothesis testing, a key statistical method.
  • Case study: Flint Water Scandal.

The Flint Water Study Case

  • Background: In 2014, Flint residents suspected their water was contaminated.
  • City's Claim: The city, backed by the Department of Environmental Quality (DEQ), claimed compliance with federal standards (less than 10% homes with water contamination > 15 ppb).
  • Residents' Response: Took own water samples, initiating the Flint Water Study (FWS).

Hypothesis Testing

  • Purpose: Determine if a population parameter differs from a claimed parameter.
  • Key Components:
    • Null Hypothesis (H₀): The current state, e.g., P = 10% (city's claim).
    • Alternate Hypothesis (Hₐ): A new idea, e.g., P > 10% (residents' claim).

Statistical Analysis

  • Population Parameter of Interest: Proportion of homes with contaminated water in Flint.
  • Observational Units: Houses in Flint.
  • Hypothesis:
    • H₀: P = 10% (less than 10% contaminated water)
    • Hₐ: P > 10% (more than 10% contaminated)
  • Sample Data: Residents found 20% contamination in a sample of 271 homes.
  • Statistical Evaluation:
    • Test the likelihood of observing a sample proportion (p-hat = 20%) if H₀ is true.
    • Using normal distribution and sampling distribution, calculate the probability of p-hat ≥ 20% when true P = 10%.

Conclusion from Flint Study

  • Probability Result: Very low probability (0.000002) of observing such high contamination if city’s claim were true.
  • Decision: Reject H₀; evidence supports Hₐ.

Broader Implications

  • Systemic Change: Residents’ findings led to city action and policy changes.
  • Key Takeaways: Hypothesis testing as a tool to challenge established norms with data-backed evidence.

Important Concepts

  • Null and Alternate Hypothesis Construction:
    • H₀: Parameter equals claimed value.
    • Hₐ: Parameter is greater than, less than, or not equal to claimed value.
  • Role of Statistics: Statistics can be a powerful tool in dismantling old ideas or systems.

Reflection

  • Quote: Audre Lorde on challenging systems—statistics can be a tool in systemic change.

Summary

  • Application: Use statistics and hypothesis testing to evaluate and challenge established truths.
  • Outcome: Flint residents successfully used hypothesis testing to reveal inaccuracies in city claims.