Research Methodology - Dr. Krishan K. Pandey

296 Research Methodology
μ U
σ U
bgbg
n
=
n 1 2 ×
2
=
12 12
2
= 72
=
nn 1 2bn1 + n2
+ 1g
=
12
bgbgb 12 12 12 + 12 + 1g
12
= 17.32
As the alternative hypothesis is that the means of the two populations are not equal, a two-tailed
test is appropriate. Accordingly the limits of acceptance region, keeping in view 10% level of
significance as given, can be worked out as under:
Fig. 12.3
As the z value for 0.45 of the area under the normal curve is 1.64, we have the following limits
of acceptance region:
Upper limit = μ + 164 . σ = 72 + 164 . 17. 32 = 100. 40
U U
Limit
164 .
u u
164 .
0.05 of area 0.05 of area
0.45 of area 0.45 of area
b g
b g
u u
Lower limit = μU − 164 . σU
= 72 − 164 . 17. 32 = 4360 .
As the observed value of U is 54.5 which is in the acceptance region, we accept the null hypothesis
and conclude that the two samples come from identical populations (or that the two populations have
the same mean) at 10% level.
We can as well calculate the U statistic as under using R value:
2
b g
n2 n2
+ 1
U = n1 ⋅ n2
+
2
bgbg b g
12 12 + 1
= 12 12 + − 132. 5
2
= 144 + 78 – 132.5 = 89.5
The value of U also lies in the acceptance region and as such our conclusion remains the same, even
if we adopt this alternative way of finding U.
We can take one more example concerning U test wherein n and n are both less than 8 and as
1 2
such we see the use of table given in the appendix concerning values of Wilcoxon’s distribution
(unpaired distribution).
Limit
43.6 u 72 100.4
(Shaded portion indicates
rejection regions)
− R
2