📊

Selecting Inference Procedures in Statistics

May 6, 2025

Mostly Math: Choosing the Right Inference Procedure

Introduction

  • Host: Ashley
  • Focus: Big picture review on selecting inference procedures
  • Audience: AP Statistics students preparing for exams
  • Goal: Determine which inference procedure to use, not how to perform them

Key Questions for Choosing Inference Procedure

  1. Data Type

    • Categorical or Quantitative?
    • Categorical: Proportions
    • Quantitative: Means
  2. Type of Statistical Question

    • Hypothesis Test: Yes/No answer; sufficient/not sufficient information
    • Confidence Interval: Range of values
    • Relationship: Tests like chi-squared or regression line
  3. Sample Size

    • One sample or two samples?
    • Special Cases:
      • Difference of Means (Paired Data): Mean of differences in paired data
      • Pooled Data: Hypothesis tests with proportions assuming equal proportions (p1 = p2)

Application Examples

Example 1: Battery Lifespan

  • Question: Which brand of AA batteries lasts longer, Duracell or Energizer?
  • Data Type: Quantitative
  • Test Type: Confidence Interval
  • Sample Type: Two-sample
  • Procedure: Two-sample t interval for mean difference

Example 2: Contacts in Phones

  • Question: Does a typical senior have 250 contacts?
  • Data Type: Quantitative
  • Test Type: Hypothesis Test
  • Sample Type: One-sample
  • Procedure: One-sample t-test for means

Example 3: TikTok Usage

  • Question: What percent of students at your school are on TikTok?
  • Data Type: Qualitative
  • Test Type: Confidence Interval
  • Sample Type: Single
  • Procedure: Confidence interval for a proportion

Example 4: Relationship Between Speed and Survival

  • Question: Is there a relationship between speed and survival in a zombie apocalypse?
  • Data Type: Quantitative
  • Test Type: Relationship
  • Procedure: T-test or interval for the slope of a regression line

Example 5: Political Party and College Type

  • Question: Is there a relationship between political party and college type?
  • Data Type: Qualitative
  • Test Type: Relationship
  • Procedure: Chi-squared test for association

Example 6: iPod Ownership

  • Question: Who is more likely to own an iPod, Gen Z or Millennials?
  • Data Type: Qualitative
  • Test Type: Confidence Interval
  • Sample Type: Two-sample
  • Procedure: Two-sample z interval for proportions

Example 7: Doomscrolling Duration

  • Question: How long do 16-18 year-olds spend doomscrolling?
  • Data Type: Quantitative
  • Test Type: Confidence Interval
  • Sample Type: One-sample
  • Procedure: One-sample t interval for mean

Example 8: Skittles Color Distribution

  • Question: Are Skittles colors equally distributed?
  • Data Type: Qualitative
  • Test Type: Homogeneity
  • Procedure: Chi-squared test for homogeneity

Example 9: Razor Effectiveness

  • Question: Which brand of razor gives a closer shave?
  • Data Type: Quantitative (assumed length of hair measurement)
  • Test Type: Paired Test
  • Procedure: One-sample t interval for mean of differences (paired data)

Conclusion

  • Importance of understanding the type of data, question, and sample
  • Emphasized using paired design when applicable for better results
  • Encouragement for AP students to review and practice these concepts