Question

Two sets of sample data, \(\mathrm{A}\) and \(\mathrm{B}\), are given. Without doing any calculations, indicate in which set of sample data, \(\mathrm{A}\) or \(\mathrm{B}\), there is likely to be stronger evidence of a difference in the two population means. Give a brief reason, comparing means and variability, for your answer. $$ \begin{array}{cc|cc} \hline {\text { Dataset A }} & {\text { Dataset B }} \\ \hline \text { Group 1 } & \text { Group 2 } & \text { Group 1 } & \text { Group 2 } \\ \hline 12 & 25 & 15 & 20 \\ 20 & 18 & 14 & 21 \\ 8 & 15 & 16 & 19 \\ 21 & 28 & 15 & 19 \\ 14 & 14 & 15 & 21 \\ \bar{x}_{1}=15 & \bar{x}_{2}=20 & \bar{x}_{1}=15 & \bar{x}_{2}=20 \\ \hline \end{array} $$

Short answer

Dataset B provides stronger evidence for a difference in population means because it has less variability compared to Dataset A.

Step-by-step solution

Analyze variability in Dataset A

Looking at Dataset A, the values in Group 1 and 2 range from 8 to 21 and 14 to 28, respectively. There is a clear variability in this dataset. This means that the data points are dispersed or scattered.

Analyze variability in Dataset B

Looking at Dataset B, the values in Group 1 and Group 2 range only from 14 to 16 and 19 to 21, respectively. There is less variability in this dataset. This means that the data points are closer to the mean, less dispersed or less scattered.

Compare variability

Comparing the variability of the two datasets, Dataset B has less variability. This means the values around the mean are more consistent in Dataset B than in Dataset A. Despite the mean of both datasets being the same, Dataset B has less variability, hence it provides stronger evidence for a difference in population means.