The following data, recorded in days, represent the length of time to recovery f
ID: 2960186 • Letter: T
Question
The following data, recorded in days, represent the length of time to recovery for patients randomly treated with one of the two medications to clear up severe bladder infections:
Medication 1: n1 =14; x1-bar = 17; s12 = 1.5.
Medication 2: n2 =16; x2-bar = 19; s22 = 1.8.
Find a 95% and a 99% confidence intervals for the difference 2 – 1 in the mean recovery time for the two medications. Comment on the results. Assume normal populations with equal variances. Please show all work as to how you arrived at the answer. Thanks!
Explanation / Answer
Given a=0.05, t(0.025, df=n1+n2-2=14+16-2 =28) =2.05(check student t table)
So 95% CI is
(xbar2 -xbar1) ± t*[s1^2/n1 + s2^2/n2]
--> (19-17) ± 2.05*sqrt(1.5^2/14 + 1.8^2/16)
--> ( 0.7645, 3.2354)
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Given a=0.01, t(0.005, df=n1+n2-2=14+16-2 =28) =2.76(check student t table)
So 99% CI is
(xbar2 -xbar1) ± t*[s1^2/n1 + s2^2/n2]
--> (19-17) ± 2.76*sqrt(1.5^2/14 + 1.8^2/16)
--> ( 0.3366, 3.6633)