question 15 (multiple choice worth 10 points)
(02.01h mc)

the basketball team at bakersfield high school recorded their wins and losses of the season. the table given shows the data collected, in which the relationship between wins and losses is sorted by number of points scored.

| | $\ge 100$ points | $

Question

question 15 (multiple choice worth 10 points)
(02.01h mc)

the basketball team at bakersfield high school recorded their wins and losses of the season. the table given shows the data collected, in which the relationship between wins and losses is sorted by number of points scored.

| | $\ge 100$ points | $< 100$ points | total |
|---|---|---|---|
| win | 48 | | 90 |
| loss | 6 | | |
| total | | | 100 |

does the data give evidence of an association between scoring at least 100 points during the game and the basketball team winning?

- there is a weak, negative association.
- there is a weak, positive association.
- there is a strong, positive association.
- there is a strong, negative association.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Conditional Relative Frequency", "Association in Two-Way Tables" ], "current_concepts": [ "Two-Way Frequency Tables", "Conditional Relative Frequency", "Association in Two-Way Tables" ] } ## Complete the two-way frequency table $$ \begin{aligned} &\text{Total Games} = 100\ &\text{Total Wins} = 90\ &\text{Total Losses} = 100 - 90 = 10\ &\text{Wins with } \ge 100 \text{ points} = 48\ &\text{Losses with } \ge 100 \text{ points} = 6\ &\text{Total Games with } \ge 100 \text{ points} = 48 + 6 = 54\ &\text{Wins with } < 100 \text{ points} = 90 - 48 = 42\ &\text{Losses with } < 100 \text{ points} = 10 - 6 = 4\ &\text{Total Games with } < 100 \text{ points} = 42 + 4 = 46 \end{aligned} $$ ## Calculate conditional relative frequencies $$ \begin{aligned} &P(\text{Win} \mid \ge 100 \text{ points}) = \frac{48}{54} \approx 0.889 \quad (88.9\%)\ &P(\text{Win} \mid < 100 \text{ points}) = \frac{42}{46} \approx 0.913 \quad (91.3\%)\ &P(\text{Win}) = \frac{90}{100} = 0.900 \quad (90.0\%) \end{aligned} $$ ## Determine the association $$ \begin{aligned} &P(\text{Win} \mid \ge 100 \text{ points}) \approx 88.9\%\ &P(\text{Win} \mid < 100 \text{ points}) \approx 91.3\%\ &88.9\% < 91.3\% \implies \text{Weak, negative association} \end{aligned} $$

(A) There is a weak, negative association.

(B) There is a weak, positive association.

(C) There is a strong, positive association.

(D) There is a strong, negative association.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Two-Way Frequency Tables" ] }

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QUESTION IMAGE

Question

Explanation:

Complete the two-way frequency table

Calculate conditional relative frequencies

Determine the association

Answer: