The article “The Role of Niche Breadth, Resource

Chapter 7, Problem 10SE

(choose chapter or problem)

The article “The Role of Niche Breadth, Resource Availability and Range Position on the Life History of Butterflies” (A. Komonen, A. Grapputo, et al., Oikos, 2004:41–54) describes a study of several species of butterflies found in Finland. The following table presents the mean wingspan (in mm) and the flight period, defined as the mean number of days of appearance in the winged state, for 23 species in the family Lycaenidae.

\(\begin{array}{cc||cc||cc||cc}
\hline \text { Wingspan } & \begin{array}{c}
\text { Flight } \\
\text { Period }
\end{array} & \text { Wingspan } & \begin{array}{c}
\text { Flight } \\
\text { Period }
\end{array} & \text { Wingspan } & \begin{array}{c}
\text { Flight } \\
\text { Period }
\end{array} & \text { Wingspan } & \begin{array}{r}
\text { Flight } \\
\text { Period }
\end{array} \\
\hline 35.5 & 19.8 & 25.9 & 32.5 & 28.8 & 25.9 & 28.1 & 18.5 \\
30.6 & 17.3 & 31.3 & 27.5 & 35.9 & 23.1 & 25.9 & 32.3 \\
30.0 & 27.5 & 23.0 & 31.0 & 23.0 & 53.1 & 28.8 & 29.1 \\
32.3 & 22.4 & 26.3 & 37.4 & 24.6 & 38.8 & 31.4 & 37.0 \\
23.9 & 40.7 & 23.7 & 22.6 & 28.1 & 36.5 & 28.5 & 33.7 \\
27.7 & 18.3 & 27.1 & 23.1 & 25.4 & 24.0 & & \\
\hline
\end{array}\)

a. Compute the least-squares line for predicting the flight period (y) from wingspan (x).

b. Compute 95% confidence intervals for ?0 and ?1.

c. Two butterflies differ in wingspan by 2 mm. By how much do you estimate that their flight periods will differ?

d. Can you conclude that species of butterflies with larger wingspans have shorter flight periods on average? Explain.

e. Can you conclude that the mean flight period for butterflies with a wingspan of 30mm is less than 28 days?

f. A certain butterfly species has a wingspan of 28.5 mm. Find a 95% prediction interval for its flight period.