Chapter 10.3, Problem 12E

To determine

To make: The two-way table which shows the flu vaccine totals.

Answer to Problem 12E

The conditional relative frequencies is

	Flu detected	Flu not detected
	Received vaccines	$\frac{0.14}{0.43}=0.325$	$\frac{0.29}{0.43}=0.674$
	Not received vaccines	$\frac{0.15}{0.56}=0.267$	$\frac{0.41}{0.56}=0.732$

Explanation of Solution

Given:

	Flu detected	Flu not detected	total
	Received vaccines	$16$	$33$	$49$
	Not received vaccines	$17$	$46$	$63$
total	$33$	$79$	$112$

Calculation:

From the given information, the two-way table is as follows:

	Flu detected	Flu not detected	total
	Received vaccines	$16$	$33$	$49$
	Not received vaccines	$17$	$46$	$63$
total	$33$	$79$	$112$

To find the joint relative frequencies, divide each frequency by the total number of students in the survey.

	Flu detected	Flu not detected	total
	Received vaccines	$\frac{16}{112}=0.14$	$\frac{33}{112}=0.29$	$0.43$
	Not received vaccines	$\frac{17}{112}=0.15$	$\frac{46}{112}=0.41$	$0.56$
total	$\frac{33}{112}=0.29$	$\frac{79}{112}=0.70$	$1$

To find the conditional relative frequencies, use the marginal frequency in each row.

	Flu detected	Flu not detected
	Received vaccines	$\frac{0.14}{0.43}=0.325$	$\frac{0.29}{0.43}=0.674$
	Not received vaccines	$\frac{0.15}{0.56}=0.267$	$\frac{0.41}{0.56}=0.732$

Conclusion:

From the given information, the two-way table is as follows:

	Flu detected	Flu not detected
	Received vaccines	$\frac{0.14}{0.43}=0.325$	$\frac{0.29}{0.43}=0.674$
	Not received vaccines	$\frac{0.15}{0.56}=0.267$	$\frac{0.41}{0.56}=0.732$