5. We want to compare the mean reduction in diastolic blood pressure (DBP) over

Question

5. We want to compare the mean reduction in diastolic blood pressure (DBP) over a 1-month treatment period between Drug B (new antihypertensive agent) and Drug A (standard of care) in a target population of mildly hypertensive (DBP range: 100-120 mm Hg) males aged 40-59 in City X. Select a random sample of 10 subjects from the target population who meet all inclusion/exclusion criteria and randomize 5 subjects to receive Drug A and 5 to receive Drug B (n1 5, n2-5). DBP reductions in mm Hg Drug A (1): 2,4,3,1,3 Drug B (2): 5,5,9,4,3 Perform the appropriate statistical analysis. (no Cl required)

Explanation / Answer

Given that,
mean(x)=2.6
standard deviation , s.d1=1.1402
number(n1)=5
y(mean)=5.2
standard deviation, s.d2 =2.2804
number(n2)=5
null, both treatment has a similar mean rate Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.776
since our test is two-tailed
reject Ho, if to < -2.776 OR if to > 2.776
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =2.6-5.2/sqrt((1.30006/5)+(5.20022/5))
to =-2.28
| to | =2.28
critical value
the value of |t | with min (n1-1, n2-1) i.e 4 d.f is 2.776
we got |to| = 2.2803 & | t | = 2.776
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -2.2803 ) = 0.085
hence value of p0.05 < 0.085,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -2.28
critical value: -2.776 , 2.776
decision: do not reject Ho
p-value: 0.085

evidence to support both treatment has a similar mean rate

Note: level of significance is not provided, considered at 0.05 and computed the test

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