Attitude of 250 employees towards a proposed policy of the company is as observed in the following table. Calculate the χ2 statistic. Favor Indifferent Oppose Male 68 46 36 Female 27 49 24 - Mathematics and Statistics

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Sum

Attitude of 250 employees towards a proposed policy of the company is as observed in the following table. Calculate the χ2 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 (Ri)
Male 68 46 36 150
Female 27 49 24 100
Column total (Cj) 95 95 60 250

Expected frequencies are given by

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

E11 = `(150 xx 95)/250` = 57

E12 = `(150 xx 95)/250` = 57

E13 = `(150 xx 60)/250` = 36

E21 = `(100 xx 95)/250` = 38

E22 = `(100 xx 95)/250` = 38

E23 = `(100  xx 60)/250` = 24
Table of expected frequencies.

  Favor Indifferent Oppose Row total (Ri)
Male 57 57 36 150
Female 38 38 24 100
Column total (Cj) 95 95 60 250

Now,

χ2 = `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

Concept: Chi-Square Statistic ( χ2 )
  Is there an error in this question or solution?
Chapter 4: Bivariate Frequency Distribution and Chi Square Statistic - Miscellaneous Exercise 4 [Page 54]

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 8 | Page 54

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