Chapter 10.3, Problem 11E

To determine

To make: the two way table based on the breakfast totals.

Answer to Problem 11E

the conditional relative frequencies is,

	Felt tired	Not felt tired
	Skipped breakfast	$\frac{0.071}{0.214}=0.333$	$\frac{0.143}{0.214}=0.667$
	Ate breakfast	$\frac{0.071}{0.786}=0.091$	$\frac{0.714}{0.786}=0.909$

Explanation of Solution

Given:

110 people ate breakfast

30 people skipped breakfast.

10 people felt tired who ate breakfast.

10 people felt tired who skipped breakfast

Calculation:

From the given information, the two-way table is as follows:

	Felt tired	Not felt tired	total
	Skipped breakfast	$10$	$20$	$30$
	Ate breakfast	$10$	$100$	$110$
total	$20$	$120$	$140$

To find the joint relative frequencies, divide each frequency by the total number of people in the survey.

	Felt tired	Not felt tired	total
	Skipped breakfast	$\frac{10}{140}=0.071$	$\frac{20}{140}=0.143$	$0.214$
	Ate breakfast	$\frac{10}{140}=0.071$	$\frac{100}{140}=0.714$	$0.786$
total	$\frac{20}{140}=0.143$	$\frac{120}{140}=0.857$	$1$

To find the conditional relative frequencies, use the marginal frequency in each row.

	Felt tired	Not felt tired
	Skipped breakfast	$\frac{0.071}{0.214}=0.333$	$\frac{0.143}{0.214}=0.667$
	Ate breakfast	$\frac{0.071}{0.786}=0.091$	$\frac{0.714}{0.786}=0.909$

Conclusion:

the conditional relative frequencies is,

	Felt tired	Not felt tired
	Skipped breakfast	$\frac{0.071}{0.214}=0.333$	$\frac{0.143}{0.214}=0.667$
	Ate breakfast	$\frac{0.071}{0.786}=0.091$	$\frac{0.714}{0.786}=0.909$