To analyze the situation, we need to consider the composition of the concert band members at Washington School. If 30% of the members play brass instruments, it implies that in a representative sample of 30 musicians, we would expect about 30% to be brass players, which is 9 musicians.
In Stanley's survey, he included 15 brass players and 15 other musicians, making a total of 30 musicians. This result means that there were indeed 15 more brass players in his sample than expected based on the 30% probability.
Given this analysis, we can evaluate the answer choices:
A. A sampling error occurs because all 30 of the musicians Stanley surveyed should have been brass players.
- Incorrect, as not all should be brass players.
B. A sampling error occurs because only 9 of the 30 musicians Stanley surveyed should have been brass players.
- This is the correct reasoning because, statistically, he should have had about 9 brass players in a representative sample of 30 musicians, but he surveyed 15.
C. A sampling error occurs because none of the 30 musicians Stanley surveyed should have been brass players.
- Incorrect because there are brass players in the band.
D. There is no sampling error in Stanley's survey.
- Incorrect, as there clearly is a discrepancy compared to the expected distribution.
Thus, the statement that best describes the sampling error Stanley made when gathering data is B: A sampling error occurs because only 9 of the 30 musicians Stanley surveyed should have been brass players.