Refer to Example 12, which compared two groups of seven dogs each in terms of their time interacting with their owners. The following graph shows a smoothed version of the sampling distribution of xÌ…₁- xÌ…₂derived from the permutation approach. Superimposed (in blue) is the theoretical sampling distribution of xÌ…₁- xÌ…₂if the sample sizes were large.

a. What would the mean, standard error, and approximate shape of the theoretical sampling distribution of xÌ…₁ - xÌ…₂ be if the sample sizes were large?
b. Comment on how the permutation sampling distribution of xÌ…₁ - xÌ…₂ differs from the theoretical, large-sample one.
c. Consider the one-sided alternative H_a: μ₁ > μ₂. If the actually observed difference in sample means were 100, would the P-values computed from each sampling distribution be the same or different? Explain.

Transcribed Image Text:

-100 100 -200 200 Difference X - X2