Research Methodology - Dr. Krishan K. Pandey

1 2 3 4 5
z
OR
X − X
1 2
2 2
p p 2
σ 1 σ
+
n n
1
2
is used when two samples are drawn from
different populations. In case σ p1 and σ p2 are not
known. We use σs and σ
1 s respectively in their
2
places calculating
Σd i
2
σ s1 1i 1
and
= X − X n − 1
Σd i
2
σ s2 2i 2
= X − X n − 1
Mean ( μ) Populations(s) normal t-test and the t-test for difference in means and the test statistic Paired t-test or
and test statistic difference test and
sample size small (i.e.,
n < 30 )
and
population variance(s)
unknown (but the
population variances
assumed equal in case of
test on difference between
means)
X − μ H0
t =
σ s n
with
d.f. = (n – 1)
where
X1 − X2
t =
×
2
2
Σd X1i − X1i + Σd
X2i − X2i
n1 + n2
− 2
with d.f. = (n + n – 2)
1 2
1
n1 1
+
n2
the test statistic
D − 0
t =
2 2
Σ Di − D , n
n
n − 1
with d.f = (n – 1)
where n = number of
1
2
Contd.
Testing of Hypotheses I 199