800 people were asked whether they wear glasses for reading with following results. Age Wear glasses Do not wear glasses ≤ 30 310 90 > 30 290 110 Compute the χ2 square statistic. - Mathematics and Statistics

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Sum

800 people were asked whether they wear glasses for reading with the following results.

Age Wear glasses Do not wear glasses
≤ 30 310 90
> 30 290 110

Compute the χ2 square statistic.

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Solution

Table of observed frequencies.

Age Wear glasses Do not wear glasses Row total (Ri)
≤ 30 310 90 60

> 30

290 110 400
Column total (Cj) 600 200 800

Expected frequencies are given by

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

E11 = `(400xx600)/800` = 300

E12 = `(400xx200)/800` = 100

E21 = `(400xx600)/800` = 300

E22 = `(400xx200)/800` = 100

Table of expected frequencies.

Age Wear glasses Do not wear glasses Total
≤ 30 300 100 400

> 30

300 100 400
Total 600 200 800

Now,

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

=  `((310 - 300)^2)/(300) + ((90 - 100)^2)/(100) + ((290 - 300)^2)/(300) + ((110 - 100)^2)/(100)`

= `(100)/(300) + (100)/(100) + (100)/(300) + (100)/(100)`

= `200/300+1+1`

= 0.67 + 2
= 2.67

Concept: Chi-Square Statistic ( χ2 )
  Is there an error in this question or solution?
Chapter 4: Bivariate Frequency Distribution and Chi Square Statistic - Exercise 4.2 [Page 53]

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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 4 | Page 53
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