Concept explainers
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 find: The relationship between survival and class for female passengers.
(b)
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 |
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 find: The relationship between survival and class for male passengers.
(c)
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 |
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 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.
(d)
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
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