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Fig. 2 Box plot for non survivors and survivors

The Random Variable of interest is age. Let X1 denotes age of survivors and X2 denotes the

age of non-survivors.

To answer

-value of 0.05).

Further to the above assumptions, we assume that the CDFs of X 1 and X2 have same shape.

This allows us to apply the wilcoxons rank sum test.

From the calculated p-value for Wilcoxon rank sum test (0.19), there is not enough evidence

against Ho (Ho: X1 is stochastically equal to X2).

Fig 3: ECDF for non survivors and survivors

But from the histograms and ECDF

5+ to 15, 15+ to 30, 30+ to 45, 45+ to 60, and 60+. Now, we do a chi-square test to see if

survivors and non-survivors have a homogeneous distribution across these age categories. We

get a p-value of 5.47710-6, which supports our belief that there is a difference in age

distributions of survivors and non-survivors. Now, since the sample size of survivors is 313,

and that of non-survivors is 443, we can do a z-test on problem of proportion for each age

category separately, null hypotheses being

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0-5; Survivors=

tailed tests were done wherever null was refuted.

On performing Z tests, we get the following p values, and thus the adjoining conclusions:-

Age Category P value Conclusion

0 to 5 0-5; Survivors >0-5; Non-Survivors

5+ to 15

15+ to 30

30+ to 45

45+ to 60 45-60; Survivors = 45-60; Non-Survivors

60+ 60+; Survivors < 60+; Non-Survivors

I. (a) Is there a significant difference in Age distribution between male survivors

and male non survivors?

.

We use the same approach of dividing the population into age categories to find out if there is

a dependence of survival probability on age category as done in part (1), the only difference

being that here the two samples come from Male. Chi-square p value of 1.47e-11 implies

population of male survivors and non-survivors is not homogeneous with respect to age

categories. Thus, we go ahead with 6 separate Z tests, one for each age category. Null

hypotheses being as follows:-

0-5; Male_Survivors= 0-5; Male_Non-Survivors

5-15; Male_Survivors =

60+; Male_Survivors = 60+; Male_Non-Survivors

We began with two tailed tests and single tailed tests were done wherever null was refuted.


Age

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The p-values for Lilliefors

(Kolmogorov-Smirnov) normality

test

0.0001661670 0.12109238

Shapiro-Francia normality test 0.0077707718 0.11744076

The p-values for all the tests for the two samples suggest that the samples of survivors are not

normal, whereas that of non survivors follow normal distribution (at assumed -value of

0.05).This clearly suggests that the distributions are not same. However, to reinforce on this,

we do a Kolmogorov Smirnov two sample test. This also suggests that the two samples come

from different distributions (p value = 0.01326) implying there is a significant difference in

age distributions of female survivors and dead.

We use the same approach of dividing the population into age categories to find out if there is

a dependence of

30-45; Female_Survivors = 30-45; Female_Non-Survivors

45-60; Female_Survivors = 45-60; Female_Non-Survivors

60+; Female_Survivors = 60+; Female_Non-Survivors

We began with two tailed tests and single tailed tests were done wherever null was refuted.


Age Category P value Conclusion

0 to 5

5+ to 15

15+ to 30

30+ to 45

45+ to 60

60+ 0.666 60+; Female_Survivors = 60+; Female_Non-Survivors

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The above analysis suggests that there is a significant difference in age distribution between

female survivors and female non-survivors.

II. Remark on how Age affected the Survival Probability of a passenger on board

the Titanic, based on consolidations of your findings in 1 and 2 above.

The findings in 1 and 2 above suggest that females had higher survival probability than their

counterparts. Given that the boarders are males, infants and teenagers had higher survival

probability; however, age group of 15 to 30 and above 60 years had less survival probability.

Given that the boarders are females, age group of 45 to 60 had higher survival probability.

Possible reasons could have been that females and kids were given preference in going on life

boats, old could have thought of sacrificing their lives for the young.

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IV. Is there a significant di erence in Survival Probability between the two genders?ff

Ho:No difference in the survival probability of the two genders viz. male and female

Ha: Significant difference in the survival probability of the two genders viz. male and

female (Two-sided)

Data:

The below table displays the problems data:-

Survivor Non-Survivor Total

Males 142 709 851

Females 308 154 462

Total 450 863 1313

Test adopted for testing the hypothesis:

Since its a problem of proportion and we would like to compare the survival probabilities of

male and female, we can use the following tests:

1. Fishers exact test

2. Z-test

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Fishers exact test is more powerful test in this case but we can also do a Z-test as the sample

size is large.

Conclusion: On the basis of Z-test we conclude that there is a significant difference in the

survival probability of the two genders.

We have the following data:-

Survivors Non-Survivors

Passenger Class I 193 129

Passenger Class II 119 161

Passenger Class III 138 573

The p-value of 2.210-16 suggests that there is enough evidence to reject the null hypothesis

(at -value of 0.05). It can be said that there is a significant difference between population

distributions across passenger classes.

We further break the data to compare different classes. We did single-tailed Fishers test by

taking sets of two classes at a time. This helped us find which passenger class had better

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chance of survival. It was observed that the survival probability is highest for Class I

followed by Class II with Class III having the lowest probability for survival.

The above conclusion agrees with the common knowledge that passengers in first class had

the first option to mount the lifeboats. Passengers in third class were the last to mount the

lifeboats.

VI. Is there a significant difference in Survival Probability between the two genders

even after taking the effect of Passenger Class into Account?

We make three 22 contingency tables corresponding to each class, and do Fishers test as

follows:-

Class I Survivors Non Survivors

Male 59 120

Female 134 9

We did a two sided Fishers test which yielded a p value of less than 2.2e-16, i.e., there is a

significant difference in Survival Probability between the two genders for class1. So, we did a

one-sided fishers test We did a two sided Fishers test which yielded a p-value of less than

2.2e-16, i.e., there is a significant difference in Survival Probability between the two genders

for Class II. So, we did a one-sided

Class III Survivors Non Survivors

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441

Female 80 132

We did a two sided Fishers test which yielded a p value of less than 2.2e-16, i.e., there is a

significant difference in Survival Probability between the two genders for class2. So, we did a

one-sided fishers test with alternate hypothesis being that males survival probability is

less than that of

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