Birds of many species retain the same breeding partner year after year. In some of these species, male and female partners migrate separately and spend the winter in different places, often thousands of kilometers apart. Yet they manage to find one another again each spring. In a field study of individually banded pairs of black-tailed godwits, Gunnarsson et al. (2004) recorded spring arrival dates of males and females on the breeding grounds in the year after they were observed breeding together. The data for 10 pairs are provided in the accompanying table. Arrival date is measured as the number of days since March 31.

a. Display the relationship between arrival dates of males and females in a graph. What type of graph did you use?

b. Describe the pattern in part (a) briefly. Is there a relationship? Is it positive or negative? Is it linear or nonlinear? Is it weak or strong?

c. Calculate the correlation coefficient between arrival dates of male and female godwits. Include a standard error for your estimate.

d. What does the standard error in part (c) refer to?

e. Calculate an approximate 95% confidence interval for ρ .

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Female arrival date 2424 3636 3535 3535 3838 5050 5555 5656 5757 6969 Male arrival date 2222 3535 3535 4444 4646 5050 5555 5656 5656 5959