a school principal wants to know the average number of extracurricular activities. Students in her school are involved in. She assigned a student a number from 415. Using a random number generator, she slay the 200 students to be part of the sample. She concluded that students are involved in an average of two extracurricular activities. Is the principles conclusion valid?

Question

no, because not all students in the sample have extracurricular activities
no, because two students in the sample was too large
Yes, because only those who have extracurricular activities were including an example
Yes, because they every student had an equal chance to be part of the sample. The sample size also appears to be large enough.

Answer 1

The principal's conclusion can be evaluated based on the provided options. The correct answer, in this case, would be:

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

However, it's important to note that while random sampling contributes to the validity of the conclusion, there is still the possibility that if a significant number of students have no extracurricular activities, the average might not represent the entire student body accurately. If the sample exclusively included students already known to be involved in activities, that could introduce bias. But based on the given options, the one that most closely aligns with standard sampling principles is the one selected.

For a more robust conclusion, the principal should ensure that the sample adequately represents all students' involvement in extracurricular activities, including those who do not participate at all.