Chapter 10.3, Problem 10E

To determine

To make:The two-way table which shows the joint and marginal relative frequencies.

Answer to Problem 10E

Here, the two-way table that shoes the joint and marginal relative frequencies.

	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	$\frac{33}{112}=0.29$	$\frac{79}{112}=0.70$	$1$

Explanation of Solution

Given:

49 people received a flu vaccine before the flu season

63 people did not receive the vaccine.

16 people got the fluwho receive the flu vaccine

17 got the flu who did not receive

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	$\frac{33}{112}=0.29$	$\frac{79}{112}=0.70$	$1$

Conclusion:

Therefore, the two-way table that shoes the joint and marginal relative frequencies.

	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	$\frac{33}{112}=0.29$	$\frac{79}{112}=0.70$	$1$