Focus Problem: Wood-Duck Nests In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood-duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 474 eggs in group I boxes, of which a fi eld count showed about 270 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 805 eggs in group II boxes, of which a fi eld count showed about 270 hatched.

(a) Find a point estimate pˆ1 for p1, the proportion of eggs that hatch in group I nesting boxes. Find a 95% confi dence interval for p1.

(b) Find a point estimate pˆ2 for p2, the proportion of eggs that hatch in group II nesting boxes. Find a 95% confi dence interval for p2.

(c) Find a 95% confi dence interval for p1  p2. Does the interval indicate that the proportion of eggs hatched from group I nesting boxes is higher than, lower than, or equal to the proportion of eggs hatched from group II nesting boxes?

(d) Interpretation What conclusions about placement of nesting boxes can be drawn? In the article discussed in the Focus Problem, additional concerns are raised about the higher cost of placing and maintaining group I nesting boxes. Also at issue is the cost effi ciency per successful wood duck hatch.