AP Statistics 3.14: Choosing a Chi-Square Test

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

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.

	Fewer Than 6 Months	6-10 Months	11-15 Months	16-20 Months	21 or More Months	Total
Has a Majority of Regular Baseball Cards	80	84	71	76	112	423
Has a Majority of Rare Baseball Cards	11	16	9	6	35	77
Total	91	100	80	82	147	500

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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3.14.B—Identify an appropriate testing method for comparing distributions in two-way tables of categorical data… question 1