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In a certain sample of 1000 families, 450 families are consumers of tea. Out of 600 Hindu families, 286 families consume tea. Calculate the χ^{2} statistic.
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Solution
The given data can be arranged in the following table.
Consume Tea | Do not consume Tea | Total | |
Hindu family | 286 | 600 | |
Non Hindu family | |||
Total | 450 | 1000 |
Table of observed frequencies.
Consume Tea | Do not consume Tea | Row total (R_{i}) | |
Hindu family | 286 | 314 | 600 |
Non Hindu family | 164 | 236 | 400 |
Column total (C_{j}) | 450 | 550 | 1000 |
Expected frequencies are given by
E_{ij} = `("R"_"i" xx "C""j")/"N"`
E_{11} = `(600 xx 450)/1000` = 270
E_{12} = `(600 xx 550)/1000` = 330
E_{21} = `(400 xx 450)/1000` = 180
E_{22} = `(400 xx 550)/1000` = 220
Table of expected frequencies.
Consume Tea | Do not consume Tea | Total | |
Hindu family | 270 | 330 | 600 |
Non Hindu family | 180 | 220 | 400 |
Total | 450 | 550 | 1000 |
Now,
χ^{2} = `sum[(("o"_"ij" - "E"_"ij")^2)/"E"_"ij"]`
`=((286 - 270)^2)/270 + ((314 - 330)^2)/330 + ((164 - 180)^2)/180 + ((236 - 220)^2)/220`
= `256/270 + 256/330 + 256/180 + 256/220`
= 0.948 + 0.776 + 1.422 + 1.164
= 4.31
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