7.133 Can mockingbirds learn to identify specific humans? A central question in urban ecology is why some animals adapt well to the presence of humans and others do not. The following results summarize part of a study of the northern mockingbird (Mimus polyglottos) that took place on a campus of a large university.⁴⁹ For four consecutive days, the same human approached a nest and stood 1 meter away for 30 seconds, placing his or her hand on the rim of the nest. On the fifth day, a new person did the same thing. Each day, the distance of the human from the nest when the bird flushed was recorded. This was repeated for 24 nests. The human intruder varied his or her appearance (that is, wore different clothes) over the four days. We report results for only Days 1, 4, and 5 here. The response variable is flush distance measured in meters.

1. (a) Explain why this should be treated as a matched design.

2. (b) Unfortunately, the research article does not provide the standard error of the difference, only the standard error of the mean flush distance for each day. However, we can use the general addition rule for variances (page 258) to approximate it. If we assume that the correlation between the flush distance at Day 1 and Day 4 for each nest is ρ = 0.40, what is the standard deviation for the difference in distance?

3. (c) Using your result in part (b), test the hypothesis that there is no difference in the flush distance across these two days. Use a significance level of 0.05.

4. (d) Repeat parts (b) and (c) but now compare Day 1 and Day 5, assuming a correlation between flush distances for each nest of ρ = 0.30.

5. (e) Write a brief summary of your conclusions.