At Community Hospital, the burn center is experimenting with anew plasma compress treatment. A random sample of n1 = 324 patientswith minor burns received the plasma compress treatment. Of thesepatients, it was found that 268 had no visible scars aftertreatment. Another random sample of n2 = 418 patients with minorburns received no plasma compress treatment. For this group, it wasfound that 93 had no visible scars after treatment. Let p1 be thepopulation proportion of all patients with minor burns receivingthe plasma compress treatment who have no visible scars. Let p2 bethe population proportion of all patients with minor burns notreceiving the plasma compress treatment who have no visible scars.(a) Find a 90% confidence interval for p1 − p2. (Round your answersto three decimal places.) lower limit upper limit (b) Explain themeaning of the confidence interval found in part (a) in the contextof the problem. Does the interval contain numbers that are allpositive? all negative? both positive and negative? At the 90%level of confidence, does treatment with plasma compresses seem tomake a difference in the proportion of patients with visible scarsfrom minor burns? Because the interval contains only negativenumbers, we can say that there is a higher proportion of patientswith no visible scars among those who did not receive thetreatment. Because the interval contains only positive numbers, wecan say that there is a higher proportion of patients with novisible scars among those who received the treatment. We can notmake any conclusions using this confidence interval. Because theinterval contains both positive and negative numbers, we can notsay that there is a higher proportion of patients with no visiblescars among those who received the treatment.

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 467 eggsin group I boxes, of which a field count showed about 266 hatched.Group II nesting boxes were placed in highly visible locations andgrouped closely together. There were a total of 786 eggs in groupII boxes, of which a field count showed about 270 hatched. (a) Finda point estimate p̂1 for p1, the proportion of eggs that hatch ingroup I nest box placements. (Round your answer to three decimalplaces.) p̂1 = Find a 90% confidence interval for p1. (Round youranswers to three decimal places.) lower limit upper limit (b) Finda point estimate p̂2 for p2, the proportion of eggs that hatch ingroup II nest box placements. (Round your answer to three decimalplaces.) p̂2 = Find a 90% confidence interval for p2. (Round youranswers to three decimal places.) lower limit upper limit (c) Finda 90% confidence interval for p1 − p2. (Round your answers to threedecimal places.) lower limit upper limit Does the interval indicatethat the proportion of eggs hatched from group I nest boxes ishigher than, lower than, or equal to the proportion of eggs hatchedfrom group II nest boxes? 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. Because the interval contains only positive numbers,we can say that a higher proportion of eggs hatched inwell-separated and well-hidden nesting boxes. Because the intervalcontains only negative numbers, we can say that a higher proportionof eggs hatched in highly visible, closely grouped nesting boxes.We can not make any conclusions using this confidence interval. (d)What conclusions about placement of nest boxes can be drawn? In thearticle 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 greaterproportion of wood duck eggs hatch if the eggs are laid inwell-separated, well-hidden nesting boxes. A greater proportion ofwood duck eggs hatch if the eggs are laid in highly visible,closely grouped nesting boxes. The eggs hatch equally well in bothconditions.