Question

A researcher wants to know whether or not a literacy intervention is really helping people read more proficiently. She gives a sample of students a pre-test before they start the intervention and then a post-test when they complete it. Conduct a Dependent-Samples t-test using the data below to test the hypothesis that this intervention works.

                 

	Pre-test	Post-test
	4	10
	3	8
	4	7
	5	10
	3	7
	4	8
Mean	3.833	8.333
Standard Dev	0.753	1.366

 

Answer 1

 

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 =2.571
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

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 students give pre test and post test.