A researcher wants to select 6 participants from the following data set using systematic sampling. The 12th participant is randomly selected. x=(1,2,3,4...48) 1. Find all of the selected participants. 2. How would youre answer differ if the last participant were randomly selected?
It would help if you proofread your questions before you posted them.
If the researcher only wants "6 participants," why would s/he randomly select a "12th participant"?
To select participants using systematic sampling, you need to follow a predetermined pattern. In this case, the 12th participant is randomly selected, so we'll start with that participant and select every 12th participant thereafter.
1. To find all the selected participants:
- Start with the 12th participant: x(12) = 12
- Add the common difference, which is 12, to find the 2nd participant: x(12+12) = x(24) = 24
- Continue adding 12 to the previous participant to find the subsequent participants: x(36), x(48), x(60), x(72), and x(84)
Therefore, the selected participants using systematic sampling in this case are: 12, 24, 36, 48, 60, and 72.
2. If the last participant were randomly selected, we would need to adjust the systematic sampling process accordingly. In this case, we start with the participant that was randomly selected, which is x(48).
- Subtract the common difference, which is 12, to find the previous participant: x(48-12) = x(36) = 36
- Continue subtracting 12 from the current participant to find the previous participants: x(24), x(12), x(0), x(-12), and x(-24).
Since we cannot have negative participants in this context, the selection process stops at x(-24).
Therefore, if the last participant were randomly selected, the selected participants using systematic sampling would be: 48, 36, 24, 12, 0, and -12.