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A sample of men and women who had passed their driving test either in 1st attempt or in 2nd attempt surveyed. Compute statistics. Passed in 1st Attempt 2nd attempt Men 32 28 Women 8 12 - Mathematics and Statistics

Sum

A sample of men and women who had passed their driving test either in 1st attempt or in 2nd attempt surveyed. Compute χ2 statistics.

Passed in →
First attempt Second attempt
Men 32 28
Women 8 12
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Solution

Table of observed frequencies.

Passed in → First attempt Second attempt Row total (Ri)
Men 32 28 60
Women 8 12 20
Column total (Cj) 40 40 80

Expected frequencies are given by

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

E11 = `(60xx40)/80` = 30

E12 = `(60xx40)/80` = 30

E21 = `(20xx40)/80` = 10

E22 = `(20xx40)/80` = 10

Table of expected frequencies.

Passed in → First attempt Second attempt Total
Men 30 30 60
Women 10 10 20
Total 40 40 80

Now,

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

= `((32 - 30)^2)/(30) + ((28 - 30)^2)/(30) + ((8 - 10)^2)/(10) + ((12 - 10)^2)/(10)`

= `4/30+4/30+4/10+4/10`

= `8/30+8/10`

= 0.27 + 0.8
= 1.07

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
Exercise 4.2 | Q 3 | Page 53
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