Question

At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random sample of n₁ = 308 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 = 420 patients with minor burns received no plasma compress treatment. For this group, it was found that 97 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?

We can not make any conclusions using this confidence interval.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.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.

Answer 1

1)

x1                =	268	x2                =	97
p̂1=x1/n1 =	0.8701	p̂2=x2/n2 =	0.2310
n1                       =	308	n2                       =	420
estimated difference in proportion   =p̂1-p̂2   =			0.6392
std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =			0.0281
for 90 % CI value of z=		1.645
margin of error E=z*std error =		0.0462
lower bound=(p̂1-p̂2)-E=		0.593
Upper bound=(p̂1-p̂2)+E=		0.685

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.