Maharashtra State BoardHSC Commerce 11th
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Compute χ2 statistic from the following data: Graduates Post-Graduates Male 28 22 Female 32 18 - Mathematics and Statistics

Sum

Compute χ2 statistic from the following data:

  Graduates Post-Graduates
Male 28 22
Female 32 18
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Solution

Table of observed frequencies.

  Graduates Post-Graduates Row total (Ri)
Male 28 22 50
Female 32 18 50
Column total (Cj) 60 40 100

Expected frequencies are given by

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

E11 = `(50 xx 60)/100` = 30

E12 = `(50  xx 40)/100` = 20

E21 = `(50 xx 60)/100` = 30

E22 = `(50  xx 40)/100` = 20
Table of expected frequencies.

  Graduates Post-Graduates Total
Male 30 20 50
Female 30 20 50
Total 60 40 100

Now,

χ2 = `sum[(("O"_"ij" - "E"_"ij")^2)/"E"_"ij"]`

= `((28 - 30)^2)/30 + ((22 - 20)^2)/20 + ((32 - 30)^2)/30 + ((18 - 20)^2)/20`

= `4/30 + 4/20 + 4/30 + 4/20`

= `8/30 + 8/20`

= 0.267 + 0.4
= 0.667

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 7 | Page 54
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