Question

A sample of 100 people is classified by gender (male/female) and by whether they are registered voters. The sample consists of 80 females and 20 males, and has a total of 60 registered voters. If these data were used for a chi-square test for independence, what is the expected frequency for males who are registered voters?

Answer 1

12

Explanation:

Given :

Male Female Total

Registered 60

Non registered 40

Total 20 80

Solution :

N= 100

Formula of expected frequency =
`E_(ij)=(T_i * T_j)/(N)`

`E_(ij)`= expected frequency for the ith row/jth columm.

`T_i` = total in the ith row

`T_j`= total in the jth column

N = table grand total.

So, using formula
`E_(11)=(T_1 * T_1)/(100)`

`E_(11)=(60 * 20)/(100)`

`E_(11)=12`

`E_(12)=(T_1 * T_2)/(100)`

`E_(12)=(60 * 80)/(100)`

`E_(12)=48`

`E_(21)=(T_2 * T_1)/(100)`

`E_(21)=(40 * 20)/(100)`

`E_(21)=8`

`E_(22)=(T_2 * T_2)/(100)`

`E_{22]=(80 * 40)/(100)`

`E_(22)=32`

Expected frequency table

Male Female Total

Registered 12 48 60

Non registered 8 32 40

Total 20 80

So, the expected frequency for males who are registered voters are
`E_(11)=12`