Question

you try
the table shows the movie preferences of high school and college students:
julie mistakenly calculated the conditional relative frequency for college students who like comedy as being 70%. what did julie actually calculate, and what is the correct answer?
movie preference
action drama comedy row totals
high school 40 23 12 75
college 20 51 28 99
column totals 60 74 40 174

what is the correct answer for the conditional relative frequency for college students who like comedy?
27%
28%
70%
16%

Explanation:

Step1: Identify Julie's miscalculation

Julie used the column total for comedy ($40$) as the denominator instead of the college student row total ($99$).
Expression: $\frac{28}{40} = 0.7 = 70\%$
This is the relative frequency of college students among all comedy-preferring students, not the conditional relative frequency of college students who like comedy.

Step2: Calculate correct conditional frequency

Divide the number of college students who like comedy ($28$) by the total number of college students ($99$).
Expression: $\frac{28}{99} \approx 0.2828 = 28\%$

Answer:

Julie actually calculated the relative frequency of college students among all students who prefer comedy (70%). The correct conditional relative frequency for college students who like comedy is 28% (option: 28%).