Solution-:
Here, we want to test
The row variabler and column variable are independent of each other.
Vs
The row variabler and column variable are dependent of each other.
The given frequencies table are observed frequencies
X | Y | Z | Total | |
A | 24 | 51 | 31 | 106 |
B | 24 | 54 | 29 | 107 |
Total | 48 | 105 | 60 | 213 |
(a) The corresponding expected frequencies are obtained using formula
for i=1,2,; j=1,2,3
Note: are not to be rounded-off to the integers.
The given frequencies table are expected frequencies
X | Y | Z | |
A | 23.887 | 52.254 | 29.859 |
B | 24.113 | 52.746 | 30.141 |
(b) For the chi-square test statistic for this data we proceed furtuer;
Table for
X | Y | Z | |
A | 24.113 | 49.777 | 32.184 |
B | 23.888 | 55.283 | 27.902 |
The test statistic is
(c) Table value / Critical value :-
( From statistical table or By using MS-Excel Command "=CHIINV(0.005,2)" )
Decision Rule:-
Here hence we accept at l.o.s.
(d) Conclusion:- There is not sufficient evidence to support the claim that the row and column variables are dependent.
Option (1) is correct.
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