AP Statistics 3.15: Chi-Square Test Conclusions
Justify a chi-square conclusion by comparing p-value with α and stating whether evidence supports association or different distributions.
- Syllabus
- Effective Fall 2025
- Course
- AP Statistics
3.15.D—Justify a claim about the population(s) based on the results of a chi-square test for homogeneity or independence 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.
| 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
After completing the hypothesis test described in part (c), Michelle obtains a p-value of 0.0075. Assuming the conditions for inference are met, what conclusion should Michelle make about her belief? Justify your response.
Because the p-value of 0.0075 is less than any
reasonable α level such as 0.05 or 0.10, the null
hypothesis should be rejected. The data provide
convincing statistical evidence that there is an association between months collecting baseball
cards and majority card status for all baseball
card collectors at the convention.
Essentially correct (E) if the response satisfies the following two components:
1. Provides correct comparison of the p-value to
alpha ( p-value is less than alpha) AND provides a
correct decision about the null and/or alternative
hypothesis
2. States a conclusion, in context, consistent with and in terms of the stated alternative hypothesis
in part (c) using nondefinitive language
Partially correct (P) if the response satisfies only one of the two components required for E.
Incorrect (I) if the response does not meet the
criteria for E or P.
Additional Notes
- Because no alpha value is explicitly given, a response may satisfy component 1 by stating that the p-value is small AND providing a correct decision about the null and/or alternative hypothesis.
- An explicit decision about the null hypothesis is not required to satisfy component 1.
- If an explicit decision is stated and the conclusion is inconsistent with the decision, component 1 is not satisfied.
- The decision part of component 1 may be satisfied by implying the decision within the conclusion statement (sufficient evidence/insufficient evidence for the alternative hypothesis).
- To satisfy the context in component 2 the response must include discussion of both "months spent collecting baseball cards" and "which type of card is the majority in the collection."
- If the response omits hypotheses in part (c), assume the correct alternative hypothesis is provided when scoring component 2.
- If the response states incorrect hypotheses in part (c), components 1 and 2 may be satisfied by either referring to the stated alternative hypothesis or referring to the inference question.
- Examples of nondefinitive language in component 2 include "evidence to accept the alternative," "there is evidence for the alternative," "there is not sufficient evidence for the alternative," and "Michelle should conclude that her belief is correct."
- Examples of definitive language in component 2 include "proves the null," "proves the alternative," "accepts the alternative," "there is not evidence for the alternative," "no evidence for the alternative," "therefore the alternative is true," and "there is an association."
- If components 1 and/or 2 are satisfied and the response provides an incorrect interpretation of the p-value, the score is lowered from E to P or P to I.
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