Chapter 11.4, Problem 24E

To determine

To make a two-way table with conditional relative frequencies based on column totals and conditional relative frequency that the students prefer a cartoon mascot that is a hawk.

Answer to Problem 24E

This is the correct two-way table with joint relative frequencies.

Type
Tiger	Hawk	Dragon
Style	Realistic	$\frac{0.23}{0.43}\approx 0.53$	$\frac{0.25}{0.32}\approx 0.78$	$\frac{0.17}{0.25}\approx 0.68$
Cartoon	$\frac{0.20}{0.43}\approx 0.47$	$\frac{0.07}{0.32}\approx 0.22$	$\frac{0.08}{0.25}\approx 0.32$

The conditional relative frequency that the students prefer a cartoon mascot that is a hawk is 0.22

Explanation of Solution

Given information :

The information provided in the two-way table.

Formula Used :

Joint relative frequencies are found out by dividing each joint frequency by the total number of observations in the two-way table.

Sum up the rows of the joint relative frequencies in order to arrive at the marginal relative frequencies.

Divide the joint relative frequencies with the marginal relative frequencies to get the resulting two-way table.

Calculation :

Total number of observations is

  $67+74+51+58+18+24=292$

Hence the correct table of joint relative frequencies is

For instance, the joint relative frequency of mascot of realistic style of tiger type is

  $\frac{67}{292}\approx 0.23$ .

The correct calculation is

Type
Tiger	Hawk	Dragon	Marginal Frequency
Style	Realistic	$\frac{67}{292}\approx 0.23$	$\frac{74}{292}\approx 0.25$	$\frac{51}{292}\approx 0.17$	0.65
Cartoon	$\frac{58}{292}\approx 0.20$	$\frac{18}{292}\approx 0.07$	$\frac{24}{292}\approx 0.08$	0.35
Marginal Frequency	0.43	0.32	0.25	1

Next, divide the joint relative frequencies by the marginal relative frequencies on the column totals.

Type
Tiger	Hawk	Dragon
Style	Realistic	$\frac{0.23}{0.43}\approx 0.53$	$\frac{0.25}{0.32}\approx 0.78$	$\frac{0.17}{0.25}\approx 0.68$
Cartoon	$\frac{0.20}{0.43}\approx 0.47$	$\frac{0.07}{0.32}\approx 0.22$	$\frac{0.08}{0.25}\approx 0.32$

The conditional relative frequency that the students prefer a cartoon mascot that is a hawk is 0.22