Research Methodology - Dr. Krishan K. Pandey

Testing of Hypotheses I 221
of success in sample two b$p2g is due to fluctuations of random sampling. In other words, we take
the null hypothesis as H0: p$ 1= p$
2 and for testing the significance of difference, we work out the
test statistic as under:
z =
where $p 1 = proportion of success in sample one
and
$p 2 = proportion of success in sample two
q$ = 1 − p$
1 1
q$ = 1−
p$
2 2
n 1 = size of sample one
n 2 = size of sample two
pq $ 1$ 1 pq $ $
n n
1
p$ − p$
1 2
p$ ⋅ q$
p$ ⋅q$
1 1 +
n n
1
2 2
+
2 2
= the standard error of difference between two sample proportions.
2
*
Then, we construct the rejection region(s) depending upon the H a for a given level of significance
and on its basis we judge the significance of the sample result for accepting or rejecting H 0 . We can
now illustrate all this by examples.
Illustration 6
A drug research experimental unit is testing two drugs newly developed to reduce blood pressure
levels. The drugs are administered to two different sets of animals. In group one, 350 of 600 animals
tested respond to drug one and in group two, 260 of 500 animals tested respond to drug two. The
research unit wants to test whether there is a difference between the efficacy of the said two drugs
at 5 per cent level of significance. How will you deal with this problem?
* This formula is used when samples are drawn from two heterogeneous populations where we cannot have the best
estimate of the common value of the proportion of the attribute in the population from the given sample information. But
on the assumption that the populations are similar as regards the given attribute, we make use of the following formula for
working out the standard error of difference between proportions of the two samples:
where p
0
n ⋅ p$ + n ⋅ p$
=
n + n
q = 1−
p
1 1 2 2
0 0
1 2
S.E. Diff . p1− p2
=
p ⋅ q
n
0 0
1
2
p0⋅ q0
+
n
= best estimate of proportion in the population
2