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 field 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 field count showed about 270 hatched.
(a) Find a point estimate 1 for p1, the proportion of eggs that hatch in group I nesting boxes. Find a 95% confidence interval for p1.
(b) Find a point estimate 2 for p2, the proportion of eggs that hatch in group II nesting boxes. Find a 95% confidence interval for p2.
(c) Find a 95% confidence 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) 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 efficiency per successful wood duck hatch.