Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
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.

Advertisement Remove all ads

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?
Advertisement Remove all ads

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
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×