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Attitude of 250 employees towards a proposed policy of the company is as observed in the following table. Calculate the χ^{2} statistic.
Favor | Indifferent | Oppose | |
Male | 68 | 46 | 36 |
Female | 27 | 49 | 24 |
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Solution
Table of observed frequencies
Favor | Indifferent | Oppose | Row total (R_{i}) | |
Male | 68 | 46 | 36 | 150 |
Female | 27 | 49 | 24 | 100 |
Column total (C_{j}) | 95 | 95 | 60 | 250 |
Expected frequencies are given by
E_{ij} = `("R"_"i" xx "C""j")/"N"`
E_{11} = `(150 xx 95)/250` = 57
E_{12} = `(150 xx 95)/250` = 57
E_{13} = `(150 xx 60)/250` = 36
E_{21} = `(100 xx 95)/250` = 38
E_{22} = `(100 xx 95)/250` = 38
E_{23} = `(100 xx 60)/250` = 24
Table of expected frequencies.
Favor | Indifferent | Oppose | Row total (R_{i}) | |
Male | 57 | 57 | 36 | 150 |
Female | 38 | 38 | 24 | 100 |
Column total (C_{j}) | 95 | 95 | 60 | 250 |
Now,
χ^{2} = `sum[(("O"_"ij" - "E"_"ij")^2)/"E"_"ij"]`
`=((68-57)^2)/57 + ((46-57)^2)/57 + ((36-36)^2)/36 + ((27-38)^2)/38 + ((49-38)^2)/38 + ((24-24)^2)/24`
= `121/57 + 121/57 + 0 + 121/38 + 121/38 + 0`
= `242/57 + 242/38`
= 4.246 + 6.368
= 10.614
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