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

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.

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.

No, because 200 students in the sample is too large.

Answer 1

The most valid response to the principal's conclusion 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 option reflects the principles of random sampling, where every student had an equal opportunity to be selected, which helps ensure that the sample is representative of the larger population. Even though the principal must ensure that the sample accurately includes students who participate in activities, 200 students is generally a sufficiently large sample size for statistical inference in most contexts.