Chapter 13: Case Study on Plastic Pollution and Hypothesis Testing

Overview

• Focus on a case study regarding plastic pollution.
• Introduction to hypothesis testing for sample means.
  • One-sample t-test: testing if a population mean equals a known constant.
  • Two-sample t-test: testing if two populations have the same sample mean.

Problem 1: Corporations and Plastic Pollution

• Discussion on which corporations contribute the most to plastic pollution.

Hypothesis Testing and T Distribution

• Review of the T distribution in hypothesis testing.
• Comparison to hypothesis testing of proportions.
• Introduction of null and alternate hypotheses.
• Identification of assumptions for hypothesis testing.

Data Set on Plastics

• Data set generated by an international volunteer effort.
• Break Free from Plastic initiative: volunteer-based brand audits.
  • In 2020, 15,000 volunteers from 55 countries conducted audits.
  • Top polluters named: Coca-Cola, PepsiCo, Nestle, Unilever, Mondelez International.

Understanding Plastic Types

• Video link and data set links provided in course module.
• Types of plastics: PET, PP, PS, PVC.
• Recycling Codes on plastics indicate recyclability.
  • Challenge: Not all plastics are recyclable multiple times.

Analyzing the Data Set

• Different types of plastics listed in the data set.
• Categories such as HDPE and LDPE mentioned.
• Importance of understanding data headings and categories.

Dashboard Analysis

• Use of a dashboard to analyze data quickly.
• Selection of a country for deeper analysis.
• Example with the United States:
  • Total plastics recorded in 2019 and 2020.
  • Identification of top polluters.

Problem Solving and Data Manipulation

• Steps provided for deeper data analysis, if time permits.
• Pre-prepared data set focusing on Coca-Cola.

Research Question: Coca-Cola's Plastic Pollution

• Coca-Cola claims an average of 275 items per country.
• Research question: Is the actual average different from 275?

Hypothesis Testing Steps

• Part A: Testing a mean (average) not a proportion.
• Part B: Use the T distribution for hypothesis testing.

T Distribution and Conditions

• Understanding T distribution: many T distributions exist based on sample size.
• Conditions for one-sample t-test:
  • Random sample assumption.
  • Sample size threshold (n ≥ 30) or normally distributed data.

Visualization

• Creation of a histogram to visualize the data.
• Description of the data's shape and spread.
  • Noted skewness and outliers in the data.

Verifying Conditions

• Verification of random sampling and sample size adequacy.

Writing Hypotheses

• Null and alternate hypotheses for the research question:
  • Null Hypothesis (H0): μ = 275
  • Alternate Hypothesis (HA): μ ≠ 275
  • Definition of μ as the average number of plastic items per country from Coca-Cola.

Two-Sample Hypothesis Example

• New research question comparing 2019 and 2020 data.
• Determination of a two-sample t-test.
  • Hypotheses involve μ1 and μ2 for different years.
  • μ1 for 2019 and μ2 for 2020.

Conclusion

• Overview of the statistical approach to addressing real-world issues like plastic pollution.
• Encouragement to use reputable sources and understand data collection methods.