In a certain sample of 1000 families, 450
families are consumers of tea. Out of 600
Hindu families, 286 families consume tea.
Calculate x statistic.
Answers
Answer:
Let us find the row and column totals and total frequency from the given 2×2 contingency table.
Expected frequencies are given by
E
ij
=
N
R
i
×C
j
Therefore,
E
11
=
N
R
1
×C
1
=
1000
600×450
=270,
E
12
=
N
R
1
×C
2
=
1000
600×550
=330
E
21
=
N
R
2
×C
1
=
1000
400×450
=180,
E
22
=
N
R
2
×C
2
=
1000
400×550
=220
Write the table of expected frequencies
We have,
χ
2
=∑[
E
ij
(O
ij
−E
ij
)
2
]
=
270
(286−270)
2
+
330
(314−330)
2
+
180
(164−180)
2
+
220
(236−220)
2
=
270
256
+
330
256
+
180
256
+
220
256
=0.94+0.77+1.42+1.16
χ
2
=4.29.