Research Methodology - Dr. Krishan K. Pandey

1 2 3 4 5
z =
p q
0 0
p$ − p$
F
HG
1 2
1 1
+
n n
1 2
I
KJ
and q = 1 − p in which case
0 0
we calculate test statistic
variance Population(s) χ 2 -test and the test F-test and the test statistic
2 eσ pj normal, observations
are independent
statistic
2
2
σ ∑ X X n
s
i − −
1 d 1 1i
/ 1
F = =
2
2
σs2
∑d X 2i − X2i / n − 1
2
2 σ s
χ =
2
σ
bn − 1g
2 2
where σs1 is treated > σ s2
In the table the various symbols stand as under:
p
with d.f. = (n – 1) with d.f. = v 1 = (n 1 –1) for
greater variance and
d.f. = v 2 = (n 2 – 1) for smaller variance
X = mean of the sample, X 1 = mean of sample one, X 2 = mean of sample two, n = No. of items in a sample, n 1 = No. of items in sample one,
n 2 = No. of items in sample two, μ H0 = Hypothesised mean for population, σ p = standard deviation of population, σ s = standard deviation of
sample, p = population proportion, q = 1 − p , p$
= sample proportion, q$ = 1 − p$
.
Testing of Hypotheses I 201