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

	thursday	friday
7 pm	130	158
9 pm	75	162
11 pm	42	94

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.

Explanation:

Step1: Calculate total for Thursday

$61 + 130 + 75 + 42 = 308$

Step2: Calculate Thursday column relative frequencies

5 pm: $\frac{61}{308} \approx 0.198$
7 pm: $\frac{130}{308} \approx 0.422$
9 pm: $\frac{75}{308} \approx 0.244$
11 pm: $\frac{42}{308} \approx 0.136$

Step3: Calculate total for Friday

$82 + 158 + 162 + 94 = 496$

Step4: Calculate Friday column relative frequencies

5 pm: $\frac{82}{496} \approx 0.165$
7 pm: $\frac{158}{496} \approx 0.319$
9 pm: $\frac{162}{496} \approx 0.327$
11 pm: $\frac{94}{496} \approx 0.189$

Step5: Compare column relative frequencies

The relative frequencies for each time slot differ noticeably between Thursday and Friday. An association exists when column relative frequencies are not similar.

Answer:

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