Question

Discuss what areas in psychology would benefit from using a paired-sample t test to better understand that phenomena. For example, when measuring intelligence, we could develop an intervention to help improve intelligence, and the compare before and after scores for each participant.

Answer 1

Assumed values
null, H0: Ud = 0
alternate, H1: Ud != 0
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.571
since our test is two-tailed
reject Ho, if to < -2.571 OR if to > 2.571
we use Test Statistic
to= d/ (S/√n)
where
value of S^2 = [ ∑ di^2 – ( ∑ di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = -4.5
We have d = -4.5
pooled standard deviation = calculate value of Sd= √S^2 = sqrt [ 127-(-27^2/6 ] / 5 = 1.049
to = d/ (S/√n) = -10.51
critical Value
the value of |t α| with n-1 = 5 d.f is 2.571
we got |t o| = 10.51 & |t α| =2.571
make Decision
hence Value of | to | > | t α| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -10.5097 ) = 0.0001
hence value of p0.05 > 0.0001,here we reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud != 0
test statistic: -10.51
critical value: reject Ho, if to < -2.571 OR if to > 2.571
decision: Reject Ho
p-value: 0.0001
we have enough evidence to support the claim that develop an intervention to help improve intelligence, and the compare before and after scores for each participant