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