The range of a dataset is the difference between the maximum and minimum values. Since the range of the treatment group is 8, this means that the maximum value minus the minimum value for that group equals 8.
For the population's range to be greater than, equal to, or less than the treatment group's range of 8, we need to consider the possible maximum and minimum values that can exist in the population.
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If the population has a range of 12: This is possible if the population includes values that extend beyond the treatment group's minimum and maximum values.
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If the population has a range of 2: This is only possible if the population values are tightly clustered and do not extend to the extent of the treatment group's range, which is less than the treatment group's range.
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If the population has a range of 6: Similar to the range of 2, this would also indicate that the population is more tightly clustered than the treatment group, making it unlikely to be the case unless the population has characteristics specifically leading to that range.
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If the population has a range of 8: This means that the population range is equal to or includes values equivalent to those of the treatment group.
Based on the reasoning, the potential ranges that could represent the population's range include:
- 12 (a broader range)
- 8 (equal to the treatment group's range)
The ranges of 2 and 6 are not suitable for the population as they imply a tighter clustering than the treatment group and would exclude the treatment group values.
Therefore, the possible population ranges can be 12 or 8.