Question

At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random sample of n1 = 324 patients with minor burns received the plasma compress treatment. Of these patients, it was found that 268 had no visible scars after treatment. Another random sample of n2 = 418 patients with minor burns received no plasma compress treatment. For this group, it was found that 93 had no visible scars after treatment. Let p1 be the population proportion of all patients with minor burns receiving the plasma compress treatment who have no visible scars. Let p2 be the population proportion of all patients with minor burns not receiving the plasma compress treatment who have no visible scars. (a) Find a 90% confidence interval for p1 − p2. (Round your answers to three decimal places.) lower limit upper limit (b) Explain the meaning of the confidence interval found in part (a) in the context of the problem. Does the interval contain numbers that are all positive? all negative? both positive and negative? At the 90% level of confidence, does treatment with plasma compresses seem to make a difference in the proportion of patients with visible scars from minor burns? Because the interval contains only negative numbers, we can say that there is a higher proportion of patients with no visible scars among those who did not receive the treatment. Because the interval contains only positive numbers, we can say that there is a higher proportion of patients with no visible scars among those who received the treatment. We can not make any conclusions using this confidence interval. Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of patients with no visible scars among those who received the treatment.

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 467 eggs in group I boxes, of which a field count showed about 266 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 786 eggs in group II boxes, of which a field count showed about 270 hatched. (a) Find a point estimate p̂1 for p1, the proportion of eggs that hatch in group I nest box placements. (Round your answer to three decimal places.) p̂1 = Find a 90% confidence interval for p1. (Round your answers to three decimal places.) lower limit upper limit (b) Find a point estimate p̂2 for p2, the proportion of eggs that hatch in group II nest box placements. (Round your answer to three decimal places.) p̂2 = Find a 90% confidence interval for p2. (Round your answers to three decimal places.) lower limit upper limit (c) Find a 90% confidence interval for p1 − p2. (Round your answers to three decimal places.) lower limit upper limit Does the interval indicate that the proportion of eggs hatched from group I nest boxes is higher than, lower than, or equal to the proportion of eggs hatched from group II nest boxes? Because the interval contains both positive and negative numbers, we can not say that a higher proportion of eggs hatched in well-separated and well-hidden nesting boxes. Because the interval contains only positive numbers, we can say that a higher proportion of eggs hatched in well-separated and well-hidden nesting boxes. Because the interval contains only negative numbers, we can say that a higher proportion of 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 the article discussed in the Focus Problem, additional concerns are raised about the higher cost of placing and maintaining group I nest box placements. Also at issue is the cost efficiency per successful wood duck hatch. No conclusion can be made. A greater proportion of wood duck eggs hatch if the eggs are laid in well-separated, well-hidden nesting boxes. A greater proportion of wood duck eggs hatch if the eggs are laid in highly visible, closely grouped nesting boxes. The eggs hatch equally well in both conditions.

Answer 1

#1) Given : n₁ = 324 , x₁ = 268 and n₂ = 418, x₂ = 93

We are asked to find 90% confidence interval for P₁-P₂  

We can use TI-84 calculator

Press STAT ----> Scroll to TESTS --->Scroll down to 2-Prop Z Interval and hit enter.

Plug the given values accordingly.

a)

Lower limit = 0.557

Upper limit = 0.653

b)

Because the interval contains only positive numbers, we can say that there is a higher proportion of patients with no visible scars among those who received the treatment. We can not make any conclusions using this confidence interval.