Chapter 11.4, Problem 26E

To determine

To find an association between participating in a sport and watching TV.

Answer to Problem 26E

There is a relationship between watching TV and participating in sports as the relationship is approximately $71\%$ .

		Participate in Sports
		Yes	No
Watch TV	Yes	$\frac{0.34}{0.48}\approx 0.71$	$\frac{0.36}{0.52}\approx 0.69$
	No	$\frac{0.14}{0.48}\approx 0.29$	$\frac{0.16}{0.52}\approx 0.31$

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

		Participate in Sports
		Yes	No	Total
Watch TV	Yes	$34\%$	$36\%$	$70\%$
	No	$14\%$	$16\%$	$55\%$
	Total	$48\%$	$52\%$	$100\%$

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

		Participate in Sports
		Yes	No
Watch TV	Yes	$\frac{0.34}{0.48}\approx 0.71$	$\frac{0.36}{0.52}\approx 0.69$
	No	$\frac{0.14}{0.48}\approx 0.29$	$\frac{0.16}{0.52}\approx 0.31$

Hence, there is a relationship between watching TV and participating in sports as the relationship is approximately $71\%$ .