Question

All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High-frequency EM radiation is thought to be a cause of cancer. The lower frequencies associated with household current are generally assumed to be harmless. To investigate the relationship between current configuration and type of cancer, researchers visited the addresses of a random sample of children who had died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either a high-current configuration (HCC) or a low-current configuration (LCC). Here are the data:

Computer software was used to analyze the data. The output included the value ${\mathrm{X}}^2=0.435$

Which of the following is the appropriate degrees of freedom for the ${\mathrm{X}}^2$test?

a. $1$

b. $2$

c. $3$

d. $4$

e. $5$

Short answer

Option(b) $2$ is the appropriate degrees of freedom for the ${\mathrm{X}}^2$ test

Step-by-step solution

Given information

We need to find appropriate degree of freedom.

		Type of	cancer
Wiring		Leukemia	Lymphoma	Other	Total
configuration	HCC	$52$	$10$	$17$	$79$
	LCC	$84$	$21$	$31$	$136$
	Total	$136$	$31$	$48$	$215$

Simplify

As the table given in step 1 :

It has $2$rows $\mathrm{r}=2$

It has $3$columns $c=3$

Degree of freedom : $(r-1)(c-1)$

$\mathrm{df}=(2-1)(3-1)=2$

Hence, the appropriate degree of freedom is $2$.