Question

five individuals with high blood pressure were given a new drug to see if it would lower their blood pressure. systolic blood pressure was measured before and after treatment for each individual. the results are below.

before: person 1= 170 person 2= 164 person 3= 168 person 4= 158 person 5= 183

after: person 1= 145 person 2= 132 person 3= 129 perosn 4= 135 perosn 5= 145

construct a 95% confidence interval for mean reduction in systolic blood pressure, round to one decimal place.

perform a hypothesis test at a 0.05 level on significance to determine if treatment for each individual. what is the pvalue round to the fourth decimal place.

do you reject the null, fail to reject the null or accept the null.

Answer 1

a.
Confidence Interval
CI = d ± t a/2 * (Sd/ Sqrt(n))
Where,
d = ∑ di/n
Sd = Sqrt( ∑ di^2 – ( ∑ di )^2 / n ] / ( n-1 ) )
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
d = ( ∑ di/n ) =157/5=31.4
Pooled Sd( Sd )= Sqrt [ 5143- (157^2/5 ] / 4 = 7.3
Confidence Interval = [ 31.4 ± t a/2 ( 7.3/ Sqrt ( 5) ) ]
= [ 31.4 - 2.776 * (3.3) , 31.4 + 2.776 * (3.3) ]
= [ 22.3 , 40.5 ]
95% confidence interval for mean reduction in systolic blood pressure = [ 22.3 , 40.5 ]
b.
Given that,
null, H0: Ud = 0
alternate, H1: Ud != 0
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.776
since our test is two-tailed
reject Ho, if to < -2.776 OR if to > 2.776
we use Test Statistic
to= d/ (S/√n)
where
value of S^2 = [ ∑ di^2 – ( ∑ di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 31.4
We have d = 31.4
pooled variance = calculate value of Sd= √S^2 = sqrt [ 5143-(157^2/5 ] / 4 = 7.301
to = d/ (S/√n) = 9.617
critical Value
the value of |t α| with n-1 = 4 d.f is 2.776
we got |t o| = 9.617 & |t α| =2.776
make Decision
hence Value of | to | > | t α| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 9.6173 ) = 0.0007
hence value of p0.05 > 0.0007,here we reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud != 0
test statistic: 9.617
critical value: reject Ho, if to < -2.776 OR if to > 2.776
decision: Reject Ho
p-value: 0.0007
we have enough evidence to support the claim that if treatment for each individual.