The number of degrees of freedom associated with the chi-square distribution in a test of independence is a. number of sample items minus 1. b. number of populations minus number of estimated parameters minus 1. c. number of populations minus 1. d. number of rows minus 1 times number of columns minus 1.

d) the number of rows minus 1 times number of columns minus 1

The degrees of freedom γ= (r-1)(s-1)

Step-by-step explanation:

chi-square distribution:-

In this chi-square test , we test if two attributes A  and B under consideration are independent or not .

here we will choose null hypothesis (H₀): Attributes are independent

Degrees of freedom :  γ= (r-1)(s-1)

where r = number of rows

and 's' = number of columns

chi - squared test

Χ² = ∑(O-E)²/ E

'O' be the observed frequency

'E' be the Expected frequency

step-by-step explanation:

5×5×5+2(8)÷2(2)+3(3)

15+16÷4+9

31÷13

do 31÷13 and u will get ur answer