Question

At Washington School, 30% of the members in the concert band play brass instruments.

Stanley conducted a survey of 15 brass players and 15 other musicians to determine the favorite song style of the members of the band.

Which statement below best describes the sampling error, if any, Stanley made when gathering data?
A.
A sampling error occurs because all 30 of the musicians Stanley surveyed should have been brass players.

B.
A sampling error occurs because only 9 of the 30 musicians Stanley surveyed should have been brass players.

C.
A sampling error occurs because none of the 30 musicians Stanley surveyed should have been brass players.

D.
There is no sampling error in Stanley's survey.

Answer 1

B.

If 30% of the band are brass players, then in a sample of 30 you would expect about 0.30 × 30 = 9 brass players. Stanley surveyed 15 brass players (50%), so his sample overrepresents brass players and introduces a sampling error.