The Data Below Were Gathered on a Random Sample of 7

Essay

The data below were gathered on a random sample of 7 male banded black-footed
albatrosses of known age. In an effort to monitor diseases of these animals, biologists
would like to be able to estimate the lifespan of healthy albatrosses in the larger
population. In males of this species gonad size (the size of the sex gland) is
associated with age. $$\begin{array}{l}\text { Gonad size vs. Age in Black-footed albatrosses }\\\begin{array} { | c | c | } \hline \begin{array} { c } \text { Gonad Size } \\\text { (sq mm) }\end{array} & \begin{array} { c } \text { Age } \\\text { (Years) }\end{array} \\\hline 42 & 1.42 \\60 & 4.75 \\20 & 0.67 \\96 & 23.64 \\24 & 0.52 \\27 & 2.35 \\27 & 1.4 \\\hline\end{array}\end{array}$$ a) What is the value of the correlation coefficient for these data?

b) What is the equation of the least squares line describing the relationship between $x =$ Gonad Size and $y =$ Age.

c) If these albatrosses are representative of the population of all albatrosses, what would you predict to be the age of a male albatross with a gonad size of $50 \mathrm { sq }$ . mm? Show any calculations below.

d) The largest albatross gonad size in the sample, $96 \mathrm { sq } \mathrm { mm }$ , is associated with an age of $23.64$ years. These animals are thought to live for up to 40 years. Would it be reasonable to use the equation from part (b) above to predict the age for an albatross with a gonad size of $150 \mathrm { sq } \mathrm { mm }$ ? Why or why not?