Question

A researcher wants to evaluate the effectiveness of cognitive behavior therapy which he thinks will decrease depression scores. Prior to testing, each of n = 10 patients rated their current level of depression on a self-report survey. After attending cognitive behavior therapy for a month, a second rating is recorded. The data are as follows:

           Before   After

                                                5          2

                                                7          7

                                                10         7

                                                14         10

            

Do the results indicate a significant difference? Use α = .01. If so, what percent of the decrease is actually due to the therapy?

Answer 1

Given that,
null, H0: Ud = 0
alternate, H1: Ud != 0
level of significance, α = 0.01
from standard normal table, two tailed t α/2 =5.841
since our test is two-tailed
reject Ho, if to < -5.841 OR if to > 5.841
we use Test Statistic
to= d/ (S/√n)
where
value of S^2 = [ ∑ di^2 – ( ∑ di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 2.5
We have d = 2.5
pooled variance = calculate value of Sd= √S^2 = sqrt [ 34-(10^2/4 ] / 3 = 1.732
to = d/ (S/√n) = 2.887
critical Value
the value of |t α| with n-1 = 3 d.f is 5.841
we got |t o| = 2.887 & |t α| =5.841
make Decision
hence Value of |to | < | t α | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 2.8868 ) = 0.0632
hence value of p0.01 < 0.0632,here we do not reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud != 0
test statistic: 2.887
critical value: reject Ho, if to < -5.841 OR if to > 5.841
decision: Do not Reject Ho
p-value: 0.0632
we do not have enough evidence to support the claim that significant difference
percent of the decrease is actually due to the therapy is 6.32%