Question

a school principal wants to understand the general opinion of all students about a new cafeteria menu. she surveys 200 randomly chosen students from all grades. each grade level has the same number of students. how might this sample affect the results?

the sample is likely to be biased because it only includes a few students from each grade.

the sample is likely to be representative because it includes students from all grades

the sample is biased because it only includes students who like the new menu.

the sample is too large, which might lead to misleading results.

Explanation:

• Analyze Option 1: The problem states each grade has the same number of students, but we don't know how many grades there are. If there are, say, 4 grades, 200 students would be 50 per grade, which isn't necessarily "a few". So this is incorrect.
• Analyze Option 2: The sample is random and includes students from all grades. Since each grade has the same number of students, a random sample from all grades is likely to represent the opinions of all students (as it captures different grade levels' perspectives). This makes sense.
• Analyze Option 3: There's no indication the sample only includes students who like the menu. The survey is of randomly chosen students, so this is incorrect.
• Analyze Option 4: A larger sample generally gives more accurate results, not misleading ones. So this is incorrect.

Answer:

B. The sample is likely to be representative because it includes students from all grades