Chapter 13: Case Study on Plastic Pollution

Introduction

• Focus on plastic pollution and introduction to hypothesis testing.
  • One-sample t-test for population means against a constant.
  • Two-sample t-test for comparing two population means.
• Initial discussion on corporations contributing to pollution.

Hypothesis Testing

• T Distribution: Used in the context of hypothesis testing.
  • Previously seen in confidence intervals.
• Null and Alternate Hypothesis: Definitions similar to those in proportion tests.
• Assumptions: Similar to those in hypothesis testing of proportions.

Data Set on Plastics

• Origin: Volunteer effort to track plastics and their corporate origins.
• Resource: Video introduction to "Break Free from Plastic" brand audits.
• Key Polluters in 2020: Coca-Cola, PepsiCo, Nestlé, Unilever, Mondelez International.
• Responsibility: Corporations need to reduce plastic production and improve recycling.

Types of Plastics

• Plastic Codes: Identify types and recyclability.
  • PS, PP, PET, PVC, HDPE, IDPE, etc.
• Recyclability Issues: Most plastics aren't truly recyclable multiple times due to international waste management practices.

Data Analysis

• Data set includes countries and parent corporations over 2019 and 2020.
• Sample Tasks:
  • Identify types of plastics and categories.
  • Understand plastic codes and recyclability.
• Dashboard Exploration: Analyze data via interactive tools.
  • Example: Data for the USA in 2019-2020.
  • Top plastic polluters include Kroger, PepsiCo, Coca-Cola.

Hypothesis Testing Process

• Research Question: Is the average number of Coca-Cola plastics different from 275 in 2020?
• Testing Type: Mean (not proportion), use t distribution.
  • Conditions: Random samples, sample size large enough (n > 30).
• Data Visualization: Histogram and box plot for understanding data distribution.
• Writing Hypotheses:
  • Null (H₀): μ = 275
  • Alternate (H₁): μ ≠ 275

Advanced Hypothesis Testing

• New Research Question: Is 2020's average less than 2019's?
  • Requires a two-sample t-test.
• Hypotheses for Two Sample Test:
  • Null (H₀): μ₂ = μ₁
  • Alternate (H₁): μ₂ < μ₁
• Parameters: μ₁ and μ₂ represent means for 2019 and 2020 respectively.

Conditions for T-Distribution Use

• Random Samples: Assumed based on reputable data collection.
• Sample Size: Must be large enough or data normally distributed.
  • Issues with small sample sizes and skewed data.

Conclusion

• Importance of understanding data and conducting proper hypothesis testing.
• Encouragement to explore further and apply these methods to real-world questions about plastic pollution.