Question: Beavers and beetles Refer to Exercise.

(a) How many clusters of beetle larvae would you predict in a circular plot with 5 tree stumps cut by beavers? Show your work.

(b) About how far off do you expect the prediction in part (a) to be from the actual number of clusters of beetle larvae? Justify your answer.

Exercise: Beavers and beetles Do beavers benefit beetles? Researchers laid out 23 circular plots, each 4 meters in diameter, at random in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth, so that beetles prefer them. If so, more stumps should produce more beetle larvae.8 Minitab output for a regression analysis on these data is shown below. Construct and interpret a 99% confidence interval for the slope of the population regression line. Assume that the conditions for performing inference are met.

Regression Analysis: Beetle larvae versus Stumps

Predictor             Coef      SE Coef        T          P

Constant         -1.286        2.853        -0.45    0.657

Stumps            11.894       1.136        10.47    0.000

S = 6.41939     R-Sq = 83.9%     R-Sq(adj) = 83.1%