Question

Principal Watkins is conducting a study on student achievement at North Middle School. The school has 120 sixth graders, 120 seventh graders, and 185 eighth graders. Principal Watkins plans to randomly select 30 sixth graders, 30 seventh graders, and 30 eighth graders to participate in the study.

Will Principal Watkins be able to form generalizations about the school population based on the sample?

A.
no, because there were not enough students selected from eighth grade

B.
yes, because the same number of students were selected from each grade

C.
yes, because the students were randomly selected by the principal

D.
no, because all 425 students from the school should have been selected

Answer 1

A.

No. Eighth graders are underrepresented: 185 of 425 students (~43.5%) are eighth graders, but only 30 of the 90 sampled (~33.3%) are eighth graders. Because the sample is not proportional to the grade sizes, it is not representative of the whole school (unless appropriate statistical weighting is applied).