Question

A school principal wants to know the average number of extracurricular activities students in her school are involved in. She assigned each student a number from 1 to 415. Using a random number generator, she selected 200 students to be part of the sample. She concluded that students are involved in an average of two extracurricular activities. Is the principal’s conclusion valid?(1 point) Responses Yes, because every student had an equal chance to be part of the sample. The sample size also appears to be large enough. Yes, because every student had an equal chance to be part of the sample. The sample size also appears to be large enough. Yes, because only those who have extracurricular activities were included in the sample. Yes, because only those who have extracurricular activities were included in the sample. No, because not all students in the sample have extracurricular activities. No, because not all students in the sample have extracurricular activities. No, because 200 students in the sample is too large.

Answer 1

The most valid response is:

No, because not all students in the sample have extracurricular activities.

This conclusion is important because if the sample includes students who do not participate in any extracurricular activities, it could skew the average down. To accurately determine the average number of extracurricular activities per student, the sample should include students who represent the whole population in terms of participation. Including only those with extracurricular activities would give a biased view of the average for the entire student body.