Chapter 7.4, Problem 24E

To determine

To make two-way table that shows the conditional relative frequencies based on the column totals.

Also to determine conditional relative frequency that a student prefers a cartoon mascot if he or she prefers a hawk as a mascot.

Answer to Problem 24E

Two-way table that shows the conditional relative frequencies based on the column totals.

	Tiger	Hawk	Dragon
Realistic	$\frac{0.11}{0.21}\approx 0.52$	$\frac{0.13}{0.16}\approx 0.81$	$\frac{0.09}{0.13}\approx 0.69$
Cartoon	$\frac{0.10}{0.21}\approx 0.48$	$\frac{18}{584}\approx 0.03$	$\frac{0.04}{0.13}\approx 0.31$

Conditional relative frequency that a student prefers a cartoon mascot if he or she prefers a hawk as a mascot $\approx 0.03$

Explanation of Solution

Given information:

A two-way table

  

Concept used:

Conditional relative frequency is the ratio of joint relative frequency to marginal relative frequency.

Given table:

	Tiger	Hawk	Dragon	Total
Realistic	67	74	51	192
Cartoon	58	18	24	100
Total	125	92	75	292

Total

  $\begin{array}{l}=292+292\\ =584\end{array}$

Find joint relative frequency and marginal relative frequency:

	Tiger	Hawk	Dragon
Realistic	$\frac{67}{584}=0.11$	$\frac{74}{584}=0.13$	$\frac{51}{584}=0.09$
Cartoon	$\frac{58}{584}=0.10$	$\frac{18}{584}=0.03$	$\frac{24}{584}=0.04$
Total	0.21	0.16	0.13

Two-way table that shows the conditional relative frequencies based on the column totals.

	Tiger	Hawk	Dragon
Realistic	$\frac{0.11}{0.21}\approx 0.52$	$\frac{0.13}{0.16}\approx 0.81$	$\frac{0.09}{0.13}\approx 0.69$
Cartoon	$\frac{0.10}{0.21}\approx 0.48$	$\frac{18}{584}\approx 0.03$	$\frac{0.04}{0.13}\approx 0.31$

Conditional relative frequency that a student prefers a cartoon mascot if he or she prefers a hawk as a mascot $\approx 0.03$