A researcher wanted to understand the effect of a new drug on the cerebral blood
ID: 3319981 • Letter: A
Question
A researcher wanted to understand the effect of a new drug on the cerebral blood flow (CBF) in adult women. The researcher is concerned that CBF may drop to unsafe levels. An experiment was design to compare the CBF of individuals who took the new drug during the course of 1 week, and individuals who took a placebo.
Treatment Group 2.7, 2.9, 2.7, 3.9, 2.7, 2.1, 2.6, 2.2, 4.2, 5.0, 0.7, 5.3
Control Group 3.5, 2.5, 3.8, 8.1, 3.6, 2.2, 5.0, 2.9, 2.3, 2.9, 5.1
Conduct the appropriate nonparametric test BY HAND to assess whether adults who take the new medicine have a reduction of CBF compared to those who did not. Conduct the test at the = 0.05 significance level.
Explanation / Answer
Given that,
mean(x)=3.083
standard deviation , s.d1=1.3016
number(n1)=12
y(mean)=3.809
standard deviation, s.d2 =1.7282
number(n2)=11
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.23
since our test is two-tailed
reject Ho, if to < -2.23 OR if to > 2.23
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =3.083-3.809/sqrt((1.69416/12)+(2.98668/11))
to =-1.13
| to | =1.13
critical value
the value of |t | with min (n1-1, n2-1) i.e 10 d.f is 2.23
we got |to| = 1.13011 & | t | = 2.23
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.1301 ) = 0.285
hence value of p0.05 < 0.285,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -1.13
critical value: -2.23 , 2.23
decision: do not reject Ho
p-value: 0.285
we do not have enough evidence to support the claim that experiment was design to compare the CBF of individuals who took the new drug during the course of 1 week, and individuals who took a placebo
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