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
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
Answers
GPT-4o mini
To determine the best description of the sampling error in Stanley's survey, we need to analyze the situation given the information that 30% of the concert band members play brass instruments.
Out of 30 musicians surveyed (15 brass players and 15 other musicians), the expected number of brass players based on the 30% figure should be:
30% of 30 = 0.3 * 30 = 9 brass players.
This means that if the sampling was reflective of the band composition, there should have been approximately 9 brass players and 21 other musicians.
Now let's 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 musicians should be brass players.
B. A sampling error occurs because only 9 of the 30 musicians Stanley surveyed should have been brass players.
- Incorrect, as 9 brass players is indeed the expected amount based on the 30% proportion.
C. A sampling error occurs because none of the 30 musicians Stanley surveyed should have been brass players.
- Incorrect, the scenario does involve brass players.
D. There is no sampling error in Stanley's survey.
- Correct, as the number of brass players surveyed aligns with the expected proportion.
Therefore, the best statement describing the sampling error, if any, would be:
**D. There is no sampling error in Stanley's survey.**
Out of 30 musicians surveyed (15 brass players and 15 other musicians), the expected number of brass players based on the 30% figure should be:
30% of 30 = 0.3 * 30 = 9 brass players.
This means that if the sampling was reflective of the band composition, there should have been approximately 9 brass players and 21 other musicians.
Now let's 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 musicians should be brass players.
B. A sampling error occurs because only 9 of the 30 musicians Stanley surveyed should have been brass players.
- Incorrect, as 9 brass players is indeed the expected amount based on the 30% proportion.
C. A sampling error occurs because none of the 30 musicians Stanley surveyed should have been brass players.
- Incorrect, the scenario does involve brass players.
D. There is no sampling error in Stanley's survey.
- Correct, as the number of brass players surveyed aligns with the expected proportion.
Therefore, the best statement describing the sampling error, if any, would be:
**D. There is no sampling error in Stanley's survey.**