Question

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

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

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

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 appropriate response to the validity of 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 response is valid because the random selection of students helps ensure that the sample is representative of the larger population. A sample size of 200 is typically considered sufficiently large for statistical analysis, and as long as the students were selected randomly, it supports the generalizability of the findings regarding extracurricular activities. However, it’s essential to consider the possibility that if the average includes students who do not participate in any extracurricular activities, the conclusion may be skewed. But based on the provided options, the selected response is the most appropriate.