A researcher has developed a new drug designed to reduce blood pressure. In an e

Question

A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 23 subjects were assigned to the central group and received a standard, well-known treatment. After a suitable period, the reduction in blood pressure for each subject was recorded. A summary of these data is: The P-value for a two-sample t test using these data, using Option 2 for degrees of freedom, is: between 0.025 and 0.05 larger than 0.05 between 0.02 and 0.025 between 0.04 and 0.05

Explanation / Answer

Given that,
mean(x)=23.48
standard deviation , s.d1=8.01
number(n1)=21
y(mean)=18.52
standard deviation, s.d2 =7.15
number(n2)=23
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.086
since our test is two-tailed
reject Ho, if to < -2.086 OR if to > 2.086
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =23.48-18.52/sqrt((64.1601/21)+(51.1225/23))
to =2.159
| to | =2.159
critical value
the value of |t | with min (n1-1, n2-1) i.e 20 d.f is 2.086
we got |to| = 2.15898 & | t | = 2.086
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.159 ) = 0.043
hence value of p0.05 > 0.043,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 2.159
critical value: -2.086 , 2.086
decision: reject Ho
p-value: 0.043

p-value is between 0.025 to 0.05

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