Chapter 11.4, Problem 25E

To determine

To find an association between living on campus and having a car.

Answer to Problem 25E

There is an association between living in campus and having a car.

Living on Campus
Yes	No
Have a car	Yes	$\frac{0.35}{0.85}\approx 0.41$	$\frac{0.10}{0.15}\approx 0.67$
No	$\frac{0.50}{0.85}\approx 0.59$	$\frac{0.05}{0.15}\approx 0.33$

Explanation of Solution

Given information :

The information provided in the two-way table.

Formula Used :

Make a two-way table to map the joint frequencies. Use logic to complete the same. After this, use the row total of the marginal relative frequencies of either row or column to map out the conditional relative frequencies. This table would be able to conclude the relationships that have been asked in the question.

Calculation :

Two-way table for the percentages is

Living on Campus
Yes	No	Total
Have a car	Yes	$35\%$	$10\%$	$45\%$
No	$50\%$	$5\%$	$55\%$
Total	$85\%$	$15\%$	$100\%$

Next, find the marginal relative frequencies using the column total.

Living on Campus
Yes	No
Have a car	Yes	$\frac{0.35}{0.85}\approx 0.41$	$\frac{0.10}{0.15}\approx 0.67$
No	$\frac{0.50}{0.85}\approx 0.59$	$\frac{0.05}{0.15}\approx 0.33$

Hence, there is an association between living in campus and having a car.