Question

1. a school district surveyed students about whether they prefer math or english class and found that there was no association between school level (middle school, high school) and preferred class. the survey included 100 middle school students and 200 high school students. in total, 180 of the students preferred math and 120 preferred english. which two - way table represents this scenario? a) math, english, total; middle school: 50, 50, 100; high school: 130, 70, 200; total: 180, 120, 300 b) math, english, total; middle school: 40, 60, 100; high school: 140, 60, 200; total: 180, 120, 300 c) math, english, total; middle school: 80, 20, 100; high school: 100, 100, 200; total: 180, 120, 300 d) math, english, total; middle school: 60, 40, 100; high school: 120, 80, 200; total: 180, 120, 300 e) math, english, total; middle school: 90, 10, 100; high school: 90, 110, 200; total: 180, 120, 300

Explanation:

Step1: Check total number of students

The total number of middle - school students is 100 and high - school students is 200, so the total number of students is \(100 + 200=300\). Also, the total number of students who prefer math is 180 and English is 120, which sums to 300. All tables have correct row and column totals for the number of students.

Step2: Use the no - association condition

Since there is no association between school level and preferred class, the proportion of students who prefer math (or English) should be the same for middle - school and high - school students. The proportion of students who prefer math in the whole group is \(\frac{180}{300}=0.6\), and the proportion of students who prefer English is \(\frac{120}{300} = 0.4\).
For middle - school students (100 students), the number of students who prefer math should be \(100\times0.6 = 60\) and English should be \(100\times0.4=40\).
For high - school students (200 students), the number of students who prefer math should be \(200\times0.6 = 120\) and English should be \(200\times0.4 = 80\).

Answer:

D. Math: Middle school 60, High school 120; English: Middle school 40, High school 80; Total: Math 180, English 120, Total 300