which statements are supported by the data in the table? check all that apply.

- the team is twice as likely to win an away game as they are a home game.
- the team wins $\frac{3}{5}$ of their home games.
- the team wins $\frac{1}{2}$ of their games.
- the team played a total of 27 games.
- the team won a total of 6 games.
- the team lost more home games than away games.

Question

which statements are supported by the data in the table? check all that apply.

- the team is twice as likely to win an away game as they are a home game.
- the team wins $\frac{3}{5}$ of their home games.
- the team wins $\frac{1}{2}$ of their games.
- the team played a total of 27 games.
- the team won a total of 6 games.
- the team lost more home games than away games.

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 totals and proportions from the table $$ \begin{aligned} &\text{Total Home Games} = 6 + 10 = 16\ &\text{Total Away Games} = 3 + 8 = 11\ &\text{Total Wins} = 6 + 3 = 9\ &\text{Total Losses} = 10 + 8 = 18\ &\text{Total Games Played} = 16 + 11 = 27 \end{aligned} $$ ## Evaluate each statement $$ \begin{aligned} &\text{Likelihood of winning home game} = \frac{6}{16} = 0.375\ &\text{Likelihood of winning away game} = \frac{3}{11} \approx 0.273 \quad (\text{Not twice as likely})\ &\text{Proportion of home wins} = \frac{6}{16} = \frac{3}{8} e \frac{3}{5}\ &\text{Proportion of total wins} = \frac{9}{27} = \frac{1}{3} e \frac{1}{2}\ &\text{Total games played} = 27 \quad (\text{True})\ &\text{Total wins} = 9 e 6\ &\text{Home losses (10) } > \text{ Away losses (8)} \quad (\text{True}) \end{aligned} $$

The team is twice as likely to win an away game as they are a home game.

The team wins $\frac{3}{5}$ of their home games.

The team wins $\frac{1}{2}$ of their games.

The team played a total of 27 games.

The team won a total of 6 games.

The team lost more home games than away games.

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

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Question

Explanation:

Calculate totals and proportions from the table

Evaluate each statement

Answer: