Question

An ecologist hypothesizes that birds with shorter wing spans use wider tree branches. The ecologist captured male birds, measured their wing span and other characteristics in millimeters, and then marked and released them. During the ensuing winter, the ecologist repeatedly observed the marked birds as they foraged for food on tree branches. He noted the branch diameter on each occasion, and calculated the average branch diameter for each bird in centimeters. The measurement data are below. What can the ecologist conclude with an α of 0.01?

wing span	branch diameter
79.3 80.1 80.7 81.5 80.1 80.7 81.1 80.5 80.7	1.02 1.04 1.21 1.53 1.21 1.56 1.39 1.31 1.39

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected above:

b) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

There was a significant positive relationship between the wing span of the birds and branch diameter.There was a significant negative relationship between the wing span of the birds and branch diameter.    There was no significant relationship between the wing span of the birds and branch diameter.

Answer 1

Let denotes the correlation coefficient between wing span and branch diameter.

To test whether birds with shorter wing spans use wider tree branches. i.e. to test whether there is a negative correlation between wing span and branch diameter

a) The appropriate statistic - Correlation

b)

b) critical value = -2.998

The value of test statistic = 3.887

Decision : Fail to reject H0

c) Effect size = r² = 0.8267² = 0.6834, large effect

d) There was a significant negative relationship between the wing span of the birds and branch diameter.