In the Focus Problem at the beginning of this chapter, a studywas described comparing the hatch ratios of wood duck nestingboxes. Group I nesting boxes were well separated from each otherand well hidden by available brush. There were a total of 485 eggsin group I boxes, of which a field count showed about 276 hatched.Group II nesting boxes were placed in highly visible locations andgrouped closely together. There were a total of 780 eggs in groupII boxes, of which a field count showed about 270 hatched.

(a) Find a point estimate p?₁ forp₁, the proportion of eggs that hatch in groupI nest box placements. (Round your answer to three decimalplaces.)
p?₁ =

Find a 99% confidence interval for p₁. (Roundyour answers to three decimal places.)

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(b) Find a point estimate p?₂ forp₂, the proportion of eggs that hatch in groupII nest box placements. (Round your answer to three decimalplaces.)
p?₂ =

Find a 99% confidence interval for p₂. (Roundyour answers to three decimal places.)

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(c) Find a 99% confidence interval for p₁ ?p₂. (Round your answers to three decimalplaces.)

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Does the interval indicate that the proportion of eggs hatched fromgroup I nest boxes is higher than, lower than, or equal to theproportion of eggs hatched from group II nest boxes?

Because the interval contains only negative numbers, we can saythat a higher proportion of eggs hatched in highly visible, closelygrouped nesting boxes.Because the interval contains both positiveand negative numbers, we can not say that a higher proportion ofeggs hatched in well-separated and well-hidden nestingboxes.    We can not make any conclusions usingthis confidence interval.Because the interval contains onlypositive numbers, we can say that a higher proportion of eggshatched in well-separated and well-hidden nesting boxes.

(d) What conclusions about placement of nest boxes can be drawn? Inthe article discussed in the Focus Problem, additional concerns areraised about the higher cost of placing and maintaining group Inest box placements. Also at issue is the cost efficiency persuccessful wood duck hatch.

No conclusion can be made.A greater proportion of wood duck eggshatch if the eggs are laid in well-separated, well-hidden nestingboxes.    The eggs hatch equally well in bothconditions.A greater proportion of wood duck eggs hatch if the eggsare laid in highly visible, closely grouped nesting boxes.