Tom wants to know the average number of musical instruments students in his school play. He used the school’s two band classes, consisting of a total of 48 students, as his representative sample. He concluded that students in his school play an average of three musical instruments. Is his conclusion valid?

Question

Tom wants to know the average number of musical instruments students in his school play. He used the school’s two band classes, consisting of a total of 48 students, as his representative sample. He concluded that students in his school play an average of three musical instruments. Is his conclusion valid?
No, because he did not choose students randomly. 
Yes, because all members of the sample play at least one musical instrument. 
Yes, because the sample includes both males and females who play musical instruments. 
No, because his representative sample is too large.

GPT-4o mini · Answer

The correct answer is: **No, because he did not choose students randomly.** Tom's conclusion is not valid because he selected a non-random sample. The students in the band classes are likely to have different musical engagement levels compared to the general student population, leading to a biased estimate of the average number of musical instruments that all students in the school play. A truly representative sample would require random selection from the entire student body to draw valid conclusions.