AP Statistics 3.14 B Identify an Appropriate Testing Method for Comparing Distributions in Two Way Tables of Categorical Data Questions

Choose chi-square homogeneity or independence by deciding whether distributions across populations or association within one population is being tested.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • choose a chi-square test for homogeneity to compare one categorical distribution across populations
  • choose a chi-square test for independence to test association between two categorical variables
  • calculate chi-square degrees of freedom as (rows minus 1)(columns minus 1) for a two-way table

AP Statistics 3.14 B Identify an Appropriate Testing Method for Comparing Distributions in Two Way Tables of Categorical Data Questions question 1

Baseball cards are trading cards that feature data on a player's performance in baseball games. Michelle is at a national baseball card collector's convention with approximately 20,000 attendees. She notices that some collectors have both regular cards, which are easily obtained, and rare cards, which are harder to obtain. Michelle believes that there is a relationship between the number of months a collector has been collecting baseball cards and whether the majority of the cards (cards appearing more often) in their collection are regular or rare. She obtains information from a random sample of 500 baseball card collectors at the convention and records how many full months they have been collecting baseball cards and whether the majority of the cards in their card collection are regular or rare. Her results are displayed in a two-way table.

Majority Type of Baseball Cards and Months of Collecting Baseball Cards

Majority Type of Baseball Cards and Months of Collecting Baseball Cards

Michelle believes there is a relationship between the number of months spent collecting baseball cards and which type of card is the majority in the collection (regular or rare).

Name the hypothesis test Michelle should use to investigate her belief. Do not perform the hypothesis test.

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