Chapter 1.1, Problem 38E

a.

To determine

To find the distributions of survival status for males and for females within each class of travel. To determine and explain whether women survive the disaster at higher rates than men.

Answer to Problem 38E

The results of the survival status for males and for females within each class of travel is as shown in the table below:

Survival Status	First Class		Second Class		Third Class
	Female	Male	Female	Male	Female	Male
Survived	97.22%	32.57%	86.02%	8.33%	46.06%	16.23%
Dead	2.78%	67.43%	13.98%	91.67%	53.94%	83.77%

Yes, the above table indicates that women survive the disaster at higher rates than men in each class of travel.

Explanation of Solution

The below table summarizes data on survival status by gender and class of travel on the Titanic:

Survival Status	First Class		Second Class		Third Class
	Female	Male	Female	Male	Female	Male
Survived	140	57	80	14	76	75
Dead	4	118	13	154	89	387

Let us first determine the column total of each column, which is the sum of all counts in the corresponding column as shown in table below:

Survival Status	First Class		Second Class		Third Class
	Female	Male	Female	Male	Female	Male
Survived	140	57	80	14	76	75
Dead	4	118	13	154	89	387
Column Total	140+4=144	57+118=175	80+13=93	14+154=168	76+89=165	75+387=462

To determine the distribution of survival status for each gender within each class of travel, we divide the counts by the column total as shown below:

Survival Status	First Class		Second Class		Third Class
	Female	Male	Female	Male	Female	Male
Survived	$\frac{140}{144}\approx 97.22\%$	$\frac{57}{175}\approx 32.57\%$	$\frac{80}{93}\approx 86.02\%$	$\frac{14}{168}\approx 8.33\%$	$\frac{76}{165}\approx 46.06\%$	$\frac{75}{462}\approx 16.23\%$
Dead	$\frac{4}{144}\approx 2.78\%$	$\frac{118}{175}\approx 67.43\%$	$\frac{13}{93}\approx 13.98\%$	$\frac{154}{168}\approx 91.67\%$	$\frac{89}{165}\approx 53.94\%$	$\frac{387}{462}\approx 83.77\%$

We note that for each class, the female survival rate is higher than the male survival rate (97.22% versus 32.57% for first class, 86.02% versus 8.33% for second class and 46.06% versus 16.23% for third class), which indicates that women survive the disaster at higher rates than men.

b.

To determine

To determine the relationship between the survival rate for both males and females in all three classes of travel and verify whether it holds the similar relation such as first-class passengers had the highest survival rate, while third-class passengers had the lowest survival rate.

Answer to Problem 38E

The results of the survival status for males and for females within each class of travel is as shown in the table below:

Survival Status	First Class		Second Class		Third Class
	Female	Male	Female	Male	Female	Male
Survived	97.22%	32.57%	86.02%	8.33%	46.06%	16.23%
Dead	2.78%	67.43%	13.98%	91.67%	53.94%	83.77%

No, the above table indicates that the same relationship does not hold good for both males and females in all three classes of travel with respect to the survival rate in different classes.

Explanation of Solution

The below table summarizes data on survival status by gender and class of travel on the Titanic:

Survival Status	First Class		Second Class		Third Class
	Female	Male	Female	Male	Female	Male
Survived	140	57	80	14	76	75
Dead	4	118	13	154	89	387

Let us first determine the column total of each column, which is the sum of all counts in the corresponding column as shown in table below:

Survival Status	First Class		Second Class		Third Class
	Female	Male	Female	Male	Female	Male
Survived	140	57	80	14	76	75
Dead	4	118	13	154	89	387
Column Total	140+4=144	57+118=175	80+13=93	14+154=168	76+89=165	75+387=462

To determine the distribution of survival status for each gender within each class of travel, we divide the counts by the column total as shown below:

Survival Status	First Class		Second Class		Third Class
	Female	Male	Female	Male	Female	Male
Survived	$\frac{140}{144}\approx 97.22\%$	$\frac{57}{175}\approx 32.57\%$	$\frac{80}{93}\approx 86.02\%$	$\frac{14}{168}\approx 8.33\%$	$\frac{76}{165}\approx 46.06\%$	$\frac{75}{462}\approx 16.23\%$
Dead	$\frac{4}{144}\approx 2.78\%$	$\frac{118}{175}\approx 67.43\%$	$\frac{13}{93}\approx 13.98\%$	$\frac{154}{168}\approx 91.67\%$	$\frac{89}{165}\approx 53.94\%$	$\frac{387}{462}\approx 83.77\%$

We note that the female survival rate is highest for first class (97.22%) and lowest for third class (46.06%). However, for males, we note that the lowest survival rate is for second class (8.33%) instead of for third class (16.23%). Thus, the same relationship does not hold good for both males and females in all three classes of travel.