In a study of the tufted titmouse (Parus bicolor), an ecologist captured seven male birds, measured their wing lengths and other characteristics, and then marked and released them. During the ensuing winter, he repeatedly observed the marked birds as they foraged for insects and seeds on tree branches. He noted the branch diameter on each occasion, and calculated (from 50 observations) the average branch diameter for each bird. The results are shown in the table.35

(a) Calculate se and specify the units. Verify the approximate relationship between sY and se, and r.
(b) Do the data provide sufficient evidence to conclude that the diameter of the forage branches chosen by male titmice is correlated with their wing length? Test an appropriate hypothesis against a nondirectional alternative. Let a = 0.05.
(c) The test in part (a) was based on 7 observations, but each branch diameter value was the mean of 50 observations. If we were to test the hypothesis of part (a) using the raw numbers, we would have 350 observations rather than only 7. Why would this approach not be valid?

Transcribed Image Text:

Wing lengthBranch diameter Bird X (mm) Y (em) 79.0 80.0 81.5 84.0 79.5 82.5 83.5 81.429 102 104 1.20 151 1.21 .56. 1.29 12614 021035 Mean SD 1.98806 r 0.80335 SS (resid) 0094 I 5