Resource managers of forest game lands were concerned about the size of the deer and rabbit populations during the winter months in a particular forest. As an estimate of population size, they proposed using the average number of pellet groups for rabbits and deer per 30-foot-square plots. From an aerial photograph, the forest was divided into N= 10,000 30-foot-square grids. A simple random sample of 2 = 500 plots was taken, and the number of pellet groups was observed for rabbits and for deer. The results of this study are summarized in the accompanying table.

a. Estimate $\mu}_{1},{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}{\mu}_{2$, the average number of pellet groups for deer and rabbits, respectively, per 30-foot-square-plots. Place bounds on the errors of estimation.

b. Estimate the difference in the mean size of pellet groups per plot for the two animals, with an appropriate margin of error.

Deer

Sample mean = 2.30

Sample variance = 0.65

Rabbits

Sample mean = 4.52

Sample variance = 0.97