Chapter 10.3, Problem 4E

To determine

To calculate:

The values from the incomplete two-way table:

		Response		Total
		Yes	No
Role	Student	$56$
	Teacher		$7$	$10$
Total			$49$

Answer to Problem 4E

The completed two-way table is as follows:

		Response		Total
		Yes	No
Role	Student	$56$	$42$	$98$
	Teacher	$3$	$7$	$10$
Total		$59$	$49$	$108$

Explanation of Solution

Given information:

A partial survey report is given about the preference of female students to take a gym class or choir.

		Response		Total
		Yes	No
Role	Student	$56$
	Teacher		$7$	$10$
Total			$49$

Calculation:

For completion of the given table, first number the columns and rows as follows:

		Response		Total
		Yes	No
Role	Student	$\left(\text{1},\text{1}\right)$	$\left(\text{1},\text{2}\right)$	$(1,3)$
	Teacher	$\left(\text{2},1\right)$	$\left(\text{2},\text{2}\right)$	$\left(\text{2},\text{3}\right)$
Total		$\left(\text{3},\text{1}\right)$	$(3,2)$	$(3,3)$

Now, let’s find the missing numbers i.e. $\left(\text{1},2\right)$ , $\left(\text{1},3\right)$ , $\left(\text{2},\text{1}\right)$ , $\left(\text{3},\text{1}\right)$ , $\left(\text{3},\text{3}\right)$ .

For, $\left(\text{1},\text{2}\right)$ :

  $\left(\text{1},\text{2}\right)=(3,2)-(2,2)$

Substitute the values,

  $\begin{array}{l}\left(\text{1},\text{2}\right)=49-7\\ \left(\text{1},\text{2}\right)=42\end{array}$

For, $\left(\text{1},\text{3}\right)$ :

  $\left(\text{1},3\right)=(1,1)+(1,2)$

Substitute the values,

  $\begin{array}{l}\left(\text{1},3\right)=56+42\\ \left(\text{1},3\right)=98\end{array}$

For, $\left(\text{2},\text{1}\right)$ :

  $\left(\text{2},\text{1}\right)=(2,3)-(2,2)$

Substitute the values,

  $\begin{array}{l}\left(\text{2},\text{1}\right)=10-7\\ \left(\text{2},\text{1}\right)=3\end{array}$

For, $\left(\text{3},\text{1}\right)$ :

  $\left(3,\text{1}\right)=(1,1)+(2,1)$

Substitute the values,

  $\begin{array}{l}\left(3,1\right)=56+3\\ \left(3,1\right)=9\end{array}$

For, $\left(\text{3},\text{3}\right)$ :

  $\left(\text{3},3\right)=(3,1)+(3,2)$

Substitute the values,

  $\begin{array}{l}\left(\text{3},3\right)=59+49\\ \left(\text{3},3\right)=108\end{array}$

Thus, putting the respected values in the table, the completed table is as follow:

		Response		Total
		Yes	No
Role	Student	$56$	$42$	$98$
	Teacher	$3$	$7$	$10$
Total		$59$	$49$	$108$