Sampling distribution of 1 2 Refer to Example 12, which compared two groups of seven dogs each in…

Sampling distribution of 1  2 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 1  2 derived from the permutation approach. Superimposed (in blue) is the theoretical sampling distribution of 1  2 if the sample sizes were large.

a. What would the mean, standard error, and approximate shape of the theoretical sampling distribution of 1  2 be if the sample sizes were large?

b. Comment on how the permutation sampling distribution of 1  2 differs from the theoretical, large-sample one.

c. Consider the one-sided alternative Ha: 1  2. 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.

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