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 expected count of cases with lymphoma in homes with an HCC?

a. $\frac{79\times 31}{215}$

b. $\frac{10\times 21}{215}$

c. $\frac{79\times 31}{10}$

d. $\frac{136\times 31}{215}$

e. None of these

Short answer

Option(a) is the expected count of cases with lymphoma in homes with an HCC.

Step-by-step solution

Given information

We need to find the expected count of cases with lymphoma in homes with an HCC.

	Leukemia	Lymphoma	Other	Total
HCC	$52$	$10$	$17$	$79$
LCC	$84$	$21$	$31$	$136$
Total	$136$	$31$	$48$	$215$

Simplify

As given, $n=215$

We know, expected count is $\frac{r\times c}{n}$

where r is row, c is column

The expected count of cases with lymphoma in homes with an HCC :

$$\begin{gathered} r=79 \\ c=31 \\ \frac{r\times c}{n}=\frac{79\times 31}{215} \end{gathered}$$