the two-way table below describes the quality of sweatshirts and t-shirts screen printed at a local store.

quality of screen printing by item type

| | perfect | flawed |
| :--- | :---: | :---: |
| t-shirts | 90 | 6 |
| sweatshirts | 40 | 10 |

which statement best describes the relationship between the two variables?

- there is an association because the relative frequencies by row are different.
- there is an association because the relative frequencies by row are the same.
- there is no association because the relative frequencies by row are different.
- there is no association because the relative frequencies by row are the same.

Question

the two-way table below describes the quality of sweatshirts and t-shirts screen printed at a local store.

quality of screen printing by item type

| | perfect | flawed |
| :--- | :---: | :---: |
| t-shirts | 90 | 6 |
| sweatshirts | 40 | 10 |

which statement best describes the relationship between the two variables?

- there is an association because the relative frequencies by row are different.
- there is an association because the relative frequencies by row are the same.
- there is no association because the relative frequencies by row are different.
- there is no association because the relative frequencies by row are the same.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Two-Way Tables", "Categorical Data Analysis" ], "new_concepts": [], "current_concepts": [ "Two-Way Tables", "Categorical Data Analysis" ] } ## Calculate row relative frequencies $$ \begin{aligned} &\text{Total T-Shirts} = 90 + 6 = 96\ &\text{Perfect T-Shirts relative frequency} = \frac{90}{96} \approx 0.9375 \text{ (93.75\%)}\ &\text{Flawed T-Shirts relative frequency} = \frac{6}{96} \approx 0.0625 \text{ (6.25\%)}\ &\text{Total Sweatshirts} = 40 + 10 = 50\ &\text{Perfect Sweatshirts relative frequency} = \frac{40}{50} = 0.80 \text{ (80\%)}\ &\text{Flawed Sweatshirts relative frequency} = \frac{10}{50} = 0.20 \text{ (20\%)} \end{aligned} $$ ## Determine association $$ \begin{aligned} &\text{Since } 93.75\% e 80\% \text{ and } 6.25\% e 20\%, \text{ the relative frequencies by row are different.}\ &\text{Therefore, there is an association between the variables.} \end{aligned} $$

(A) There is an association because the relative frequencies by row are different.

(B) There is an association because the relative frequencies by row are the same.

(C) There is no association because the relative frequencies by row are different.

(D) There is no association because the relative frequencies by row are the same.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Categorical Data Analysis" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate row relative frequencies

Determine association

Answer: