Question

At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random sample of n1-332 patients with minor burns received the plasma compress treatment. Of these patients, it was found that 250 had no visible scars after treatment. Another random sample of n2 428 patients with minor burns received no plasma compress treatment. For this group, it was found that 87 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 99% confidence interval forP1-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 99% evel of confidence, does treatment with plasma compresses seem to make a difference in the proportion of patients ith visible cars or no u s 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. 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

Answer 1

Given : n1=332 , x1=250 , n2=428 , x2=87

The sample proportions are ,

p1=x1/n1=250/332

=0.7530

p2=x2/n2=87/428=0.2033

The pooled estimate is ,

Q=1-P=0.5566

(a) The 99% confidence interval for p1-p2 is ,

$(p_1-p_2)\pm Z_{\alpha/2}\sqrt{PQ(\frac{1}{n_1}+\frac{1}{n_2})}$

$(0.7530-0.2033)\pm Z_{0.01/2}\sqrt{0.4434*0.5566(\frac{1}{332}+\frac{1}{428})}$

$0.5497\pm 2.58*0.0363$

$0.5497\pm 0.0937$

Lower limit=0.4560

Upper limit=0.6434

(b) The interval contains numbers that are all positive

Here , the interval does not contains p1-p2=0

Therefore , we can conclude that the 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 positive numbers , we can say that there is a higher proportion of patients with no visible scars among those who received the treatment .