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 200 students in the sample is too large. No, because 200 students in the sample is too large. No, because not all students in the sample have extracurricular activities.

Answer 1

The correct response is:

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

The principal's conclusion about the average number of extracurricular activities is not valid because the sample must represent the entire population of students at the school. If the sample includes students who do not participate in any extracurricular activities, the average calculated from this sample will not accurately reflect the average for the entire student population. Including only students who participate in extracurricular activities would provide a biased estimate of the average for all students.