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.

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 answer recognizes that a random sample of 200 students gives a reasonable representation of the population, assuming that the method of selection was fair and unbiased. The size of the sample is generally considered adequate for making generalizable conclusions, provided that the sampling process is sound. However, note that if there was no information about students not participating in extracurricular activities, it could introduce some bias if those students disproportionately affected the results, but the provided answers do not reflect this nuance.