# 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

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.

#### 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 )
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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 4 | Page 53