AP Statistics 3.14: Chi-Square Hypotheses

State chi-square null and alternative hypotheses by describing no difference or no association versus the contextual alternative.

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).

State the appropriate null and alternative hypotheses for the hypothesis test you identified in (c-i). Do not perform the hypothesis test.

Model Solution
$H_0$ : Months collecting cards and majority card status are independent for all baseball card collectors at the convention.\n $H_a$ : Months collecting cards and majority card status are not independent for all baseball card collectors at the convention.

Scoring components
2. States the correct null and alternative hypotheses.
3. Includes both months collecting and majority card status in context.

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3.14.C—Identify the null and alternative hypotheses for a chi-square test for homogeneity or independence question 1