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

Responses

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.
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.

Answer 1

The most appropriate response is:

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

This response highlights the validity of using a random sample of 200 students where each student had an equal chance of selection. A sufficiently large sample can provide a reasonable estimate of the average number of extracurricular activities, assuming the sample is representative of the entire student population. However, it should be noted that if the sample inadvertently excluded students with no extracurricular activities, it could bias the results, but the question does not indicate that this is the case.