Question

A chi-square homogeneity test is to be conducted to decide whether four populations are nonhomogeneous with respect to a variable that has eight possible values. What are the degrees of freedom for the x²-statistic?

Short answer

The degrees of freedom for the x²-statistic$=21$

Step-by-step solution

Step 1. Given Information

A chi-square homogeneity test is to be conducted to decide whether four populations are nonhomogeneous with respect to a variable that has eight possible values.
That is,
Number of populations,$r=4$

Number of possible values for the variable,$c=8$

Step 2.  Finding the degrees of freedom for the x2-statistic

Degrees of freedom for the χ2-statistic is given by

$$\begin{gathered} df=(r-1)(c-1) \\ =(4-1)(8-1) \\ =\left(3\right)\left(7\right) \\ =21 \end{gathered}$$