Question

students in 10th and 11th grade were asked whether they have a job. the raw data was converted to relative frequencies and recorded in the table below. given the conditional relative frequency table by column, what does the 0.14 represent? \

$$\begin{tabular}{|c|c|c|c|} \\hline & \\textbf{10th grade} & \\textbf{11th grade} & \\textbf{total} \\\\ \\hline \\textbf{job} & 0.14 & 0.25 & 0.20 \\\\ \\hline \\textbf{no job} & 0.86 & 0.75 & 0.80 \\\\ \\hline \\textbf{total} & 1 & 1 & 1 \\\\ \\hline \\end{tabular}$$

\bigcirc given that a student is a 10th grader, there is a 14\\% chance he or she has a job. \bigcirc given that a student has a job, there is a 14\\% chance he or she is a 10th grader. \bigcirc 14\\% of the students surveyed are 10th graders who have a job. \bigcirc 14\\% of the students are 10th graders.

Explanation:

Step1: Recall Conditional Relative Frequency

Conditional relative frequency by column means we look at the column totals (which are 1 for each grade, since it's by column). So for the "10th Grade" column, the values are conditional on being a 10th grader.

Step2: Analyze Each Option

• Option 1: The "Job" row and "10th Grade" column is 0.14. Since it's by column (10th grade total is 1), this is \( P(\text{Job} | \text{10th Grader}) \), so 14% chance a 10th grader has a job.
• Option 2: If it were by row (job total), but the table is by column, so this is incorrect.
• Option 3: 14% of all students? No, the total of "Job" row is 0.20, so this is conditional on 10th grade, not all students.
• Option 4: 14% of all students? The "10th Grade" total column is 1 (as a proportion of 10th graders), but overall total for 10th graders would be part of the grand total (1), but 0.14 is in the "Job" row, not total 10th graders.

Answer:

Given that a student is a 10th grader, there is a 14% chance he or she has a job.