the two-way table below describes the attendance at a movie theater at various times of the day.

patrons at a movie theater on thursday and friday

\begin{tabular}{|c|c|c|}
\hline
& thursday & friday \\
\hline
5 pm & 61 & 82 \\
\hline
7 pm & 130 & 158 \\
\hline
9 pm & 75 & 162 \\
\hline
11 pm & 42 & 94 \\
\hline
\end{tabular}

which statement best describes the relationship between the two variables?

there is an association because the relative frequencies by column are different.
there is an association because the relative frequencies by column are similar.
there is no association because the relative frequencies by column are different.
there is no association because the relative frequencies by column are similar.

Question

the two-way table below describes the attendance at a movie theater at various times of the day.

patrons at a movie theater on thursday and friday

\begin{tabular}{|c|c|c|}
\hline
 & thursday & friday \\
\hline
5 pm & 61 & 82 \\
\hline
7 pm & 130 & 158 \\
\hline
9 pm & 75 & 162 \\
\hline
11 pm & 42 & 94 \\
\hline
\end{tabular}

which statement best describes the relationship between the two variables?

there is an association because the relative frequencies by column are different.
there is an association because the relative frequencies by column are similar.
there is no association because the relative frequencies by column are different.
there is no association because the relative frequencies by column are similar.

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", "Relative Frequency" ] } ## Calculate column totals $$ \begin{aligned} \text{Thursday Total} &= 61 + 130 + 75 + 42 = 308 \ \text{Friday Total} &= 82 + 158 + 162 + 94 = 496 \end{aligned} $$ ## Calculate relative frequencies by column $$ \begin{aligned} \text{Thursday relative frequencies:} \ 5\text{ pm} &\approx \frac{61}{308} \approx 0.198 \ 7\text{ pm} &\approx \frac{130}{308} \approx 0.422 \ 9\text{ pm} &\approx \frac{75}{308} \approx 0.244 \ 11\text{ pm} &\approx \frac{42}{308} \approx 0.136 \ \ \text{Friday relative frequencies:} \ 5\text{ pm} &\approx \frac{82}{496} \approx 0.165 \ 7\text{ pm} &\approx \frac{158}{496} \approx 0.319 \ 9\text{ pm} &\approx \frac{162}{496} \approx 0.327 \ 11\text{ pm} &\approx \frac{94}{496} \approx 0.190 \end{aligned} $$ ## Determine association based on relative frequencies $$ \begin{aligned} &\text{Since the relative frequencies by column are different (e.g., } 0.422 e 0.319 \text{ and } 0.244 e 0.327\text{),} \ &\text{there is an association between the day of the week and the attendance time.} \end{aligned} $$

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

(B) There is an association because the relative frequencies by column are similar.

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

(D) There is no association because the relative frequencies by column are similar.

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

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QUESTION IMAGE

Question

Explanation:

Calculate column totals

Calculate relative frequencies by column

Determine association based on relative frequencies

Answer: