The following data, recorded in days, represents the recovery time, for patients

he298c 2021-09-21 Answered

The following data, recorded in days, represents the recovery time, for patients who are randomly treated with one of two medications to cure servere bladder infections:
Medication 1Medication 2n1=13n2=16x¯1=20x¯2=15s12=2.0s22=1.8
Find the 99% confidence interval for μ1μ2, the difference in mean drug recovery times, and INTERPRET it to get a helpful conclusion about the drugs.
Assume normal populations, with equal variances.

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Expert Answer

Jozlyn
Answered 2021-09-22 Author has 85 answers
Step 1
Given data:
n1=13,
x1=20
σ12=1,
σ1=1
n2=16,
x2=15,
σ22=1.8
σ2=1.34
Confidence level =99%
The formula for confidence interval is:
C.I.=X±Z×σn
For the sample 1:
Put the values for sample 1:
C.I.=X±Z×σn
C.I.=20±2.5758×113
C.I.=20±0.714
C.I.=[19.282.71]
Step 2
For sample 2 the CI is:
C.I.=X±Z×σn
C.I.=15±2.5758×1.3416
C.I.=15±0.863
C.I.=[14.1415.86]
For μ1μ2:
μ1μ2=X1X2±Z(σ12n1σ22n2)
μ1μ2=2015±2.77(0.45)
μ1μ2=5±1.24
μ1μ2=[3.766.24]
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