The range of a treatment group can provide information about the population from which it is sampled, but it doesn't necessarily limit the range of the entire population. The population's range could be equal to, greater than, or potentially less than the range of the treatment group, depending on the variability in the population as a whole.
Given that the range of the treatment group is 8, we can evaluate the options for the population's range:
-
8: This is a valid possibility as the population could have the same range as the treatment group.
-
6: This is also a valid possibility, as the population's range can be less than the treatment group's range, though it would imply that some of the extreme values observed in the treatment group are not present in the population.
-
2: This could be valid as well, indicating a much tighter clustering of values in the population than in the treatment group.
-
12: This is a valid possibility too, as the population could have a greater range than the treatment group. The population might have values that extend beyond those found in the treatment group.
In summary, all options are feasible, but the population range must be at least as large as the range observed in the treatment group of 8 for the sampling to have captured the full variability of the population. The potential options for the range of the population are thus:
- 8
- 6 (as it's less)
- 2 (as it's less)
- 12 (as it's more)
In conclusion, the ranges of 8 and 12 are the most straightforwardly possible given the treatment group's range of 8. However, 6 and 2 are also theoretically possible based on specific population characteristics.