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A sample of boys and girls were asked to choose their favourite sport, with the following results. Find the value of the χ2 statistic. Football Cricket Hockey Basketball Boys 86 60 44 10 Girls 40 30 - Mathematics and Statistics

Sum

A sample of boys and girls were asked to choose their favourite sport, with the following results. Find the value of the χ2 statistic.

  Football Cricket Hockey Basketball
Boys 86 60 44 10
Girls 40 30 25 5
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Solution

Table of observed frequencies.

  Football Cricket Hockey Basketball Row total (Ri)
Boys 86 60 44 10 200
Girls 40 30 25 5 100
Column total (Cj) 126 90 69 15 300

Expected frequencies are given by

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

E11 = `(200 xx 126)/300` = 84

E12 = `(200 xx 90)/300` = 60          

E13 = `(200 xx 69)/300` = 46          

E14 = `(200 xx 15)/300` = 10          

E21 = `(100 xx 126)/300` = 42

E22 = `(100 xx 90)/300` = 30

E23 = `(100 xx 69)/300` = 23

E24 = `(100 xx 15)/300` = 5

Table of expected frequencies.

  Football Cricket Hockey Basketball Total
Boys 84 60 46 10 200
Girls 42 30 23 5 100
Total 126 90 69 15 300

Now,

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

`=((86 - 84)^2)/84 + ((60 - 60)^2)/60 + ((44 - 46)^2)/46 + ((10 - 10)^2)/10 + ((40 - 42)^2)/42 + ((30 - 30)^2)/30 + ((25 - 23)^2)/23 + ((5 - 5)^2)/5`

= `4/84 + 0 + 4/46 + 0 + 4/42 + 0 + 4/23 + 0`

= 0.048 + 0.087 + 0.095 + 0.174
= 0.404

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 10 | Page 55
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