Chapter 11.4, Problem 23E

To determine

To make a two-way table with conditional relative frequencies based on row totals and the conditional relative frequency that shows the employees prefers a lunch event that is catered.

Answer to Problem 23E

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

Menu
Potluck	Catered
Meal	Lunch	$\frac{0.18}{0.42}\approx 0.43$	$\frac{0.24}{0.42}\approx 0.57$
Dinner	$\frac{0.22}{0.58}\approx 0.38$	$\frac{0.36}{0.58}\approx 0.62$

The conditional relative frequency that the employee prefers a catered event during lunch is 0.57

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.

Total number of observations is

  $36+48+44+72=200$

Hence the correct table of joint relative frequencies is

For instance, the joint relative frequency of potluck being preferred in lunch is

  $\frac{36}{200}\approx 0.18$ .

The correct calculation is

Menu
Potluck	Catered	Total
Meal	Lunch	$\frac{36}{200}\approx 0.18$	$\frac{48}{200}\approx 0.24$	0.42
Dinner	$\frac{44}{200}\approx 0.22$	$\frac{72}{200}\approx 0.36$	0.58
Total	0.40	0.60	1

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

Menu
Potluck	Catered
Meal	Lunch	$\frac{0.18}{0.42}\approx 0.43$	$\frac{0.24}{0.42}\approx 0.57$
Dinner	$\frac{0.22}{0.58}\approx 0.38$	$\frac{0.36}{0.58}\approx 0.62$

Thus, the conditional relative frequency that the employee prefers a catered event during lunch is 0.57