Question
The football and soccer teams at Juan’s middle school are selling movie tickets. He wants to determine the average number of tickets sold at the school. First, he surveyed eight random players on the football team. Then, he surveyed every third athlete on the football and soccer team. Which sampling technique should produce a more representative sample?
The first sampling method, surveying eight random football players, is the most representative.
Neither sample will be representative.
Both samples should be exactly the same.
The second sampling method, surveying the both teams, is the most representative.
The first sampling method, surveying eight random football players, is the most representative.
Neither sample will be representative.
Both samples should be exactly the same.
The second sampling method, surveying the both teams, is the most representative.
Answers
GPT-4o mini
To determine which sampling technique should produce a more representative sample, we should consider the characteristics of each method.
1. **Surveying Eight Random Players from the Football Team:** This technique involves selecting a small, random group from just one team (the football team). While the randomness can help avoid bias, the sample is limited to one team, which may not accurately reflect the entire population of athletes across both teams.
2. **Surveying Every Third Athlete on Both Teams:** This method includes a wider range of participants from both teams, potentially capturing a more diverse set of responses. By surveying athletes from both the football and soccer teams, this method reduces the risk of bias that might occur by only looking at one team. It also ensures that the sample size is larger, thus providing a better overall representation of the total population.
Based on these considerations, the second sampling method (surveying every third athlete on both teams) should produce a more representative sample. Therefore, the correct answer is:
**The second sampling method, surveying both teams, is the most representative.**
1. **Surveying Eight Random Players from the Football Team:** This technique involves selecting a small, random group from just one team (the football team). While the randomness can help avoid bias, the sample is limited to one team, which may not accurately reflect the entire population of athletes across both teams.
2. **Surveying Every Third Athlete on Both Teams:** This method includes a wider range of participants from both teams, potentially capturing a more diverse set of responses. By surveying athletes from both the football and soccer teams, this method reduces the risk of bias that might occur by only looking at one team. It also ensures that the sample size is larger, thus providing a better overall representation of the total population.
Based on these considerations, the second sampling method (surveying every third athlete on both teams) should produce a more representative sample. Therefore, the correct answer is:
**The second sampling method, surveying both teams, is the most representative.**