Research Methodology - Dr. Krishan K. Pandey

Chi-square Test 235
S. No. 1 2 3 4 5 6 7 8 9 10
Weight (kg.) 38 40 45 53 47 43 55 48 52 49
Can we say that the variance of the distribution of weight of all students from which the above
sample of 10 students was drawn is equal to 20 kgs? Test this at 5 per cent and 1 per cent level of
significance.
2
Solution: First of all we should work out the variance of the sample data or σ s and the same has
been worked out as under:
Table 10.1
S. No. X i (Weight in kgs.) (X i – X ) (X i – X ) 2
1 38 –9 81
2 40 –7 49
3 45 –2 04
4 53 +6 36
5 47 +0 00
6 43 –4 16
7 55 +8 64
8 48 +1 01
9 52 +5 25
10 49 +2 04
d i i 2
n = 10 ∑ Xi = 470 ∑ X − X = 280
∴ σ s
or σ s 2
X
X
=
n
∑
= ∑ −
i
470
= =
10
dXiXi 2
n − 1
= 3111 . .
47 kgs.
=
280
=
10 − 1
3111 .
2 2
Let the null hypothesis be H0: σp = σs
. In order to test this hypothesis we work out the χ 2
value as under:
χ
2
2
σ s
= n − 1
2
σ
p
b g