Answer :
Let's analyze each option to see whether it represents a simple random sample:
a.) Picking out the names of every 10th person from a group of 200 people who drive a car:
- This method is known as systematic sampling. It does not qualify as a simple random sample because there is a fixed interval for selection, which means not every individual in the population has an equal chance of being selected.
b.) Selecting all the students in a group of 50 students:
- This method represents taking a census rather than a sample. In this scenario, you're including the entire population rather than a subset. Therefore, it is not a sample at all, let alone a simple random sample.
c.) Using a name generator to pick out 20 names from a group of 100 students:
- This method is an example of a simple random sample. Each student in the group of 100 has an equal chance of being selected when using a random name generator.
d.) Selecting every 15th person in a group of 100 volunteers:
- Similar to option 'a', this is another example of systematic sampling. It involves a fixed selection interval, meaning not every individual has an equal chance of being selected.
Therefore, the best example that represents a simple random sample is:
c.) Using a name generator to pick out 20 names from a group of 100 students.
a.) Picking out the names of every 10th person from a group of 200 people who drive a car:
- This method is known as systematic sampling. It does not qualify as a simple random sample because there is a fixed interval for selection, which means not every individual in the population has an equal chance of being selected.
b.) Selecting all the students in a group of 50 students:
- This method represents taking a census rather than a sample. In this scenario, you're including the entire population rather than a subset. Therefore, it is not a sample at all, let alone a simple random sample.
c.) Using a name generator to pick out 20 names from a group of 100 students:
- This method is an example of a simple random sample. Each student in the group of 100 has an equal chance of being selected when using a random name generator.
d.) Selecting every 15th person in a group of 100 volunteers:
- Similar to option 'a', this is another example of systematic sampling. It involves a fixed selection interval, meaning not every individual has an equal chance of being selected.
Therefore, the best example that represents a simple random sample is:
c.) Using a name generator to pick out 20 names from a group of 100 students.
