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)

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

Yes, because every student had an equal chance to be part of the sample. The sample size also appears to be large enough.

GPT-4o mini · Answer

The correct response is: **No, because not all students in the sample have extracurricular activities.** The conclusion drawn by the principal is not valid because if the sample includes students who may not be involved in any extracurricular activities, it could skew the average participation rate. Including students who do not participate at all would lead to an average that is not representative of those who actually do participate in extracurricular activities. For accurate results, the sample should consist solely of those students involved in extracurricular activities.