Agriculture Reference
In-Depth Information
0.05
We calculate the expected frequencies as
follows:
Let the level of significance be
α ¼
¼
PA
i
B
j
probability that an individual unit possesses both the attributes
A
i
and
B
j
¼ PA½PB
j
¼
ðA
i
Þ
N
ðB
j
Þ
N
; i ¼
1
;
2
;
3
; ...; r; j ¼
1
;
2
;
3
; ...; s;
and
e
¼
A
i
B
j
expected number of individual units possessing both the attributes
A
i
and
B
j
¼
ðA
i
ÞðB
j
Þ
N
¼ N: PA
i
B
j
:
As follows:
Groups
Cultivation
Teaching
Govt. service
Others
Total
HS
¼
90
125/280
¼
90
70/280
¼
90
52/280
¼
90
33/280
90
Graduation
¼
85
125/280
¼
85
70/281
¼
85
52/281
¼
85
33/281
85
Postgraduation
¼
105
125/280
¼
105
70/282
¼
105
52/282
¼
105
33/282
105
Total
125
70
52
33
280
The expected frequencies are as follows:
Grain shape
Govt.
service Others
Aroma
Long
Dwarf
Cultivation Teaching
Aromatic
40
50
HS
40.1786
22.50
16.7143 10.6071
Nonaromatic
45
65
Graduation
37.9464
21.25
15.7857 10.0178
Solution.
To test
H
0
: Taste and aroma are inde-
pendent of each other against
Postgraduation 46.8750
26.25
19.500
12.3750
the alternative
So,
hypothesis
H
1
: Grain shape and aroma are not
independent of each other. The test statistic
follows a
2
X
r
X
s
2
f
ij
e
ij
¼
ð
65
40
:
1786
Þ
2
2
6
χ
χ
¼
distribution with 1 d.f. Let
the
e
ij
401786
i¼
1
j¼
1
level of significance be 0.05.
So
2
22
:
5
þþ
ð
2
þ
ð
5
22
:
5
Þ
15
12
:
375
Þ
¼
51
:
3642
:
12
:
375
2
N
ða þ bÞðc þ dÞða þ cÞðb þ dÞ
:
ðad bcÞ
2
The table value of
χ
0
:
05
;
6
¼
12
:
592 is less than
2
χ
¼
2
. Hence, the test is
significant and the null hypothesis is rejected.
We can conclude that the two attributes, educa-
tional standard and the type of occupation, are
not independent of each other.
the calculated value of
χ
have to go for Yates's correction.
From the above given information, we have
We don'
t
2
200
¼
ð
40
65
50
45
Þ
2
χ
115
¼
0
:
2532
:
Example 9.28.
The following table is pertaining
to classification of rice varieties classified into
grain shape and aroma. Test whether the taste
and aroma are independent of each other or not.
90
110
85
2
The calculated value of
χ
is less than the
