Final answer:
An Independent Samples t-test should be used to analyze the brain-to-body ratio between non-migrating birds and long-distance migrants to see if the differences are statistically significant.
Step-by-step explanation:
The appropriate statistical test to analyze the brain-to-body ratio between non-migrating birds and long-distance migrants is an Independent Samples t-test. This test is used when comparing the means of two independent groups to determine if there is a statistically significant difference between them. In this case, the two groups are the non-migrating birds and the long-distance migrants, and the variable of interest is the relative brain size.