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 469 eggsin group I boxes, of which a field count showed about 262 hatched.Group II nesting boxes were placed in highly visible locations andgrouped closely together. There were a total of 804 eggs in groupII boxes, of which a field count showed about 276 hatched.
(a) Find a point estimate p̂1 forp1, the proportion of eggs that hatch in groupI nest box placements. (Round your answer to three decimalplaces.)
p̂1 =
Find a 90% confidence interval for p1. (Roundyour answers to three decimal places.)
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(b) Find a point estimate p̂2 forp2, the proportion of eggs that hatch in groupII nest box placements. (Round your answer to three decimalplaces.)
p̂2 =
Find a 90% confidence interval for p2. (Roundyour answers to three decimal places.)
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(c) Find a 90% 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 positive numbers, we can saythat a higher proportion of eggs hatched in well-separated andwell-hidden nesting boxes.Because the interval contains onlynegative numbers, we can say that a higher proportion of eggshatched in highly visible, closely grouped nestingboxes.    We can not make any conclusions usingthis confidence interval.Because the interval contains bothpositive and negative numbers, we can not say that a higherproportion of eggs hatched in well-separated and well-hiddennesting 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.
A greater proportion of wood duck eggs hatch if the eggs arelaid in highly visible, closely grouped nesting boxes.No conclusioncan be made.    A greater proportion of woodduck eggs hatch if the eggs are laid in well-separated, well-hiddennesting boxes.The eggs hatch equally well in both conditions.
