Question

the conditional relative frequency table was calculated by row using data from a survey of one stations television programming. the survey compared the target audience with the type of show, either live or recorded, over a 24-hour time period.

television programming

	live	recorded	total
children	0.5	0.5	1.0
total	≈0.583	≈0.417	1.0

which is the best description of the value 0.375 in the table?

○ given that the program was targeted at adults, there is a 37.5% chance that it was recorded.
○ given that the program was recorded, there is a 37.5% chance that it was targeted at adults.
○ 37.5% of the programs are targeted at adults.
○ 37.5% of the programs are recorded.

Explanation:

Step1: Understand Conditional Relative Frequency

Conditional relative frequency by row means we look at the proportion within a specific row. The row here is "Adult", and the column is "Recorded".

Step2: Analyze Each Option

• Option 1: In the "Adult" row, the "Recorded" relative frequency is 0.375, which is 37.5%. This means given the program is for adults, the chance it's recorded is 37.5%.
• Option 2: To find the chance a recorded program is for adults, we'd use the "Recorded" column and "Adult" row relative to the "Recorded" total, which is not 0.375 here (since 0.375 / 0.417 ≈ 0.9, not 0.375).
• Option 3: The total for "Adult" is 1.0 (100%), so 37.5% isn't the proportion of adult - targeted programs overall.
• Option 4: The total for "Recorded" is ≈0.417 (41.7%), not 37.5%.

Answer:

Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.