10.126 Symmetry of permutation distribution Refer to Example 12, which compared two groups of seven dogs each in terms of their time interacting with their owners.

Figure 10.10 showed the sampling distribution by considering all possible permutations. When n1 = n2, as here, explain why the permutation distribution based on all possible permutations is symmetric. (Hint: Consider a particular permutation for which you compute the difference in sample means. How does this difference change when all dogs that were in Group 1 are switched to Group 2 and vice versa?)