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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 2 statistic. - Mathematics and Statistics

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Sum

In a certain sample of 1000 families, 450 families are consumers of tea. Out of 600 Hindu families, 286 families consume tea. Calculate the χ2 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 (Ri)
Hindu family 286 314 600
Non Hindu family 164 236 400
Column total (Cj) 450 550 1000

Expected frequencies are given by 

Eij = `("R"_"i" xx "C""j")/"N"`

E11 = `(600 xx 450)/1000` = 270

E12 = `(600 xx 550)/1000` = 330

E21 = `(400 xx 450)/1000` = 180

E22 = `(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,

χ2 = `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

Concept: Chi-Square Statistic ( χ2 )
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 4 Bivariate Frequency Distribution and Chi Square Statistic
Miscellaneous Exercise 4 | Q 9 | Page 55
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