Question

analyzing a frequency table
a random group of high school and college students were asked if they study with or without listening to music. the frequency table below shows the results of the poll
which statements are true? check all that apply.
the table shows conditional relative frequencies by column
the table shows conditional relative frequencies by row
the conditional relative frequency that someone is in high school, given that the person prefers to study without music, is about 0.56
if someone prefers to study with music, the probability the person is in college is about 63%
if someone prefers to study with music, the probability the person is in hs is about 44%
music no music total
high school 68 65 133
college 85 51 136
total 153 116 269

Explanation:

Step1: Recall conditional - relative - frequency definitions

Conditional relative frequency by column is calculated as $\frac{\text{cell value}}{\text{column total}}$, and by row as $\frac{\text{cell value}}{\text{row total}}$. This table is not a conditional - relative - frequency table.

Step2: Calculate conditional relative frequency for "high school given no music"

The conditional relative frequency that someone is in high school, given that the person prefers to study without music is $\frac{65}{116}\approx0.56$.

Step3: Calculate probability of being in college given study with music

The probability that someone is in college, given that the person prefers to study with music is $\frac{85}{153}\approx0.555\approx56\%$, not $63\%$.

Step4: Calculate probability of being in high - school given study with music

The probability that someone is in high school, given that the person prefers to study with music is $\frac{68}{153}\approx0.444\approx44\%$.

Answer:

The conditional relative frequency that someone is in high school, given that the person prefers to study without music, is about $0.56$; If someone prefers to study with music, the probability the person is in HS is about $44\%$.