Chapter 2, Problem 173E

To determine

To find: The two-way table for survival and class for the women and other one for the survival and class for the men.

Answer to Problem 173E

Solution: The two-way table for the female titanic passengers is provided below:

Female
Class
	1	2	3	Total
Survived	139	94	106	339
Died	5	12	110	127
Total	144	106	216	466

The two-way table for the male titanic passengers is provided below:

Male
Class
	1	2	3	Total
Survived	61	25	75	161
Died	118	146	418	682
Total	179	171	493	843

Explanation of Solution

Calculation: There are total 466 female passengers and out of which 144, 106, and 216 travelled in class 1, 2, and 3, respectively. In Class 1, 139 survived and five passengers died. In class 2, 94 survived and 12 died and in class 3, 106 survived and 110 died.

There were total 843 male passengers and out of which 179, 171, and 493 travelled in class 1, 2, and 3, respectively. In Class 1, 61 had survived and 118 passengers had died. In class 2, 25 survived and 146 died and in class 3, 75 survived and 418 died.

Interpretation: From both the table, it can be concluded that the total 339 female passengers survived and 127 died. The total 161 male passengers survived and 682 died.

(b)

To determine

To find: The relationship between survival and class for female passengers.

Answer to Problem 173E

Solution: By performing the conditional distribution analysis, it is found that 96.53% of first class female passengers have been survived, 88.68% second class female passengers survived and 49.07% third class female passengers survived.

Explanation of Solution

Given: The data of female passengers of different class survival is provided, which is mentioned below in table:

Female
Class
	1	2	3	Total
Survived	139	94	106	339
Died	5	12	110	127
Total	144	106	216	466

Calculation: The conditional distribution is obtained by dividing the row or column elements by the sum of that row or column observations. The conditional distribution of ‘Survived in different class for female’ can be calculated as:

Conditional distribution ‘survival of female’
Class	First	Second	Third
Female Survived	$\frac{139}{144}=0.9653$	$\frac{94}{106}=0.8868$	$\frac{106}{216}=0.4907$

The survival of female passenger in first class is 0.9653 approximately, 0.8868 approximately in second class, and 0.4907 in third class.

The conditional distribution of ‘Survival of females in different classes’ in terms of percentage is provided below:

Conditional distribution of ‘survival of female’
Class	First	Second	Third
Female Survived	96.53%	88.68%	49.07%

Interpretation: From the table above, it can be concluded that the survived female passenger for first class is greater than the other second and third class.

(c)

To determine

To find: The relationship between survival and class for male passengers.

Answer to Problem 173E

Solution: By performing the conditional distribution analysis, it is found that 34.08% first class male passengers survived, 14.62% second class male passengers survived, and 15.21% third class male passengers survived.

Explanation of Solution

Given: The data of male passengers of different class survival is provided, which is mentioned below in table:

Male
Class
	1	2	3	Total
Survived	61	25	75	161
Died	118	146	418	682
Total	179	171	493	843

Calculation: The conditional distribution is obtained by dividing the row or column elements by the sum of that row or column observation. The conditional distribution of ‘Survived in different class for male’ can be calculated as:

Conditional distribution ‘survival of male’
Class	First	Second	Third
Male Survived	$\frac{61}{179}=0.3408$	$\frac{25}{171}=0.1462$	$\frac{75}{493}=0.1521$

The survival of male passenger in first class is 0.3408 approximately, 0.1462 approximately in second class, and 0.1521 in third class.

The conditional distribution of ‘Survival of males in different classes’ in terms of percentage is provided below:

Conditional distribution of ‘survival of male’
Class	First	Second	Third
Male Survived	34.08%	14.62%	15.21%

Interpretation: From the table above, it can be concluded that the survived male passenger for first class is greater than the other second and third class.

(d)

To determine

To explain: The comparison of analysis performed in part (b) and part (c) by considering the relationship between survival and the two explanatory variables, class and sex.

Answer to Problem 173E

Solution: The survival rate of female passenger in first, second, and third class is greater than the male passengers or it can be said that the females overall had much higher survival rates in comparison to the males.

Explanation of Solution

The survival rate of female and male passengers has been calculated in part (b) and part (c), respectively. The survival rate of female passenger in the first class is 96.53% and of male is 34.08%, so the survival rate of female is greater than male in the first class. The survival rate of female passenger in the second and third class is 88.68% and 49.07%, respectively while the survival rate of male passenger in the second and third class is 14.62% and 15.21%, respectively, which is way less than the female survival rate.