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?

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?
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. 
No, because 200 students in the sample is too large. 
Yes, because only those who have extracurricular activities were included in the sample.

GPT-4o mini · Answer

The valid 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 is correct because the principal used a random number generator to select students, which helps to ensure that every student had an equal opportunity to be included in the sample. A sample size of 200 is generally considered large enough to provide a reasonable estimate of the average number of extracurricular activities students are involved in, assuming the selection is random and representational of the whole population. However, it is important to note that if a significant number of students in the sample had no extracurricular activities at all, this could potentially bias the average. But the statement does not indicate that this was specifically the case; instead, it focuses on the sampling method and size.