Agriculture Reference
In-Depth Information
X
n
which is then compared with the value of
t ¼
d
1
n
with
ðn
1
Þ
d
:
f
:;
where
d ¼
1
d
i
s
d
n
p
i¼
t
¼
t
1
s
1
=n
1
þ t
2
s
2
=n
2
X
n
s
1
=n þ s
2
=n
2
1
n
2
¼
1
ðx
i
y
i
Þ
and
s
d
i¼
and appropriate decision is taken.
We have
1
X
n
2
1
n
¼
i¼
1
d
i
d
:
x y
s
185
175
100
7
þ
10
This
t
is known as
paired t
-test statistic and
t ¼
s
¼
r
¼
721
¼
2
:
118
:
4
:
64
8
the test is known as
paired t-test
.
1
2
n
2
n
1
þ
s
The table value of
level
of significance will be compared with the
calculated value of
t
at (
n
1) d.f. for
α
for arriving at definite
conclusion according to the nature of alter-
native hypothesis.
t
The table values of
t
at upper 5% level of
significance with (
n
1
1
¼
)6 d.f. and (
n
2
1
¼
)
7 d.f. are 1.943 and 1.895, respectively. So
Example 9.10.
To test whether a specific artifi-
cial hormonal spray has effect on fruit weight of
papaya, initial and final weights from a sample of
eight plants of a particular variety of papaya were
taken at an interval of 15 days of spray.
1
:
943
100
=
7
þ
1
:
895
64
=
8
100
42
:
917
22
t
¼
¼
=
7
þ
64
=
8
:
286
¼
1
:
926
:
t
cal
> t
, hence we can reject the null
hypothesis, that is,
Now the
Initial
wt (g)
114 113 119 116 119 116 117 118
H
1
is accepted. That means
we conclude that the body weight of breed A is
greater than that of breed B.
10.
Final
wt(g)
220 217 226 221 223 221 218 224
To Test Equality of Two Population Means
Under the Given Condition of Unknown
Population Variances
Solution.
Let
x
represent
the initial weight
from a Bivariate
and
y
the final weight. So
x y ¼ d
. Assuming
Normal Population
Let (
x
1
,
y
1
), (
x
2
,
y
2
), (
x
3
,
y
3
),
...
,(
x
n
,
y
n
)be
n
pairs of observations in a random sample
drawn from a bivariate normal distribution
with parameters
that
follow a bivariate normal distri-
bution with parameters
X
and
Y
μ
x
; μ
y
; σ
x
; σ
y
;
and
ρ
xy
,
we want to test
μ
X
; μ
y
; σ
2
X
; σ
2
y
ρ
and
where
H
0
: μ
x
¼ μ
y
against
H
1
: μ
x
<μ
y
:
μ
X
and
μ
y
are the means and
σ
2
X
; σ
2
y
are the
The test statistic under
H
0
is
t
variances and
is the population correlation
coefficient between
ρ
d
sd
=
n
.
So to test the null hypothesis
X
and
Y
¼
p
with
ðn
1
Þ
d
:
f
:
H
0
: μ
X
¼ μ
y
i
:
e
: H
0
: μ
X
μ
y
¼ μ
d
¼
0, we have the test
So
d ¼
104
:
75 and
statistic
Initial wt (g)
X
114
113
119
116
119
116
117
118
Final wt (g)
Y
220
217
226
221
223
221
218
224
X Y
(
d
)
106
104
107
105
104
105
101
106
