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Statistics and probability of the crew on the Titanic

The table below summarizes the fate of the passengers and crew. A common rule of the sea is that when a ship is threatened with sinking, women and children are the first to be saved.

Fate of passengers and crew on the Titanic:
____________________________________________________________
Men women boys girls
_____________________________________________________________
Survived 332 318 29 27
Died 1360 104 35 18
______________________________________________________________

Analyzing the results

If we examine the data, we see that 19.6% of the men (332 out of 1692) survived. 75.4% of the women (318 our of 422) survived, 45.3% of the boys (29 out of 64) survived, and 60% of the girls (27 out of 45) survived. There do appear to be differences, but are the differences really significant?

First construct a bar graph showing the percentage of survivors in each of the four categories (men, women, boy, girls,). What does the graph suggest?

Next, treat the 2223 people aboard the Titanic as a sample. We could take the position that the titanic data in the above table constitute a population and therefore shoujld not be treated as a sample, so that methods of inferential statistics do not apply. But let's stipulate that the data in the table are sample data randomly selected from the population of all theoretical people who would find themselves in the same conditions. Realistically, no other people will actually find themselves in the same conditions, but we will make that assumption for the purposes of this discussion and analysis. We can then determine whether the obvserved differences have statistical significance. Use one or more formal hypothesis tests to investigate the claim that although some men survived while some women and children died, the rule of "women and children first" was essentially followed. Identify the hypothesis test(s) used and interpret the results by addressing the claim that when the Titanic sank on its maiden voyage, the rule of "women adn children first" was essentially followed.

Include all steps in the hypothesis.

Solution Preview

See the attached file.

Statistics and probability of the crew on the Titanic.

The table below summarizes the fate of the passengers and crew. A common rule of the sea is that when a ship is threatened with sinking, women and children are the first to be saved.

Fate of passengers and crew on the titanic:
____________________________________________________________
Men women boys girls
_____________________________________________________________
Survived 332 318 29 27
Died 1360 104 35 18
______________________________________________________________

Analysing the results

If we examine the data, we see that 19.6% of the men (332 out of 1692) survived. 75.4% of the women (318 out of 422) survived, 45.3% of the boys (29 out of 64) survived, and 60% of the girls (27 out of 45) survived. There do appear to be differences, but are the differences really significant?

First construct a bar graph showing the percentage of survivors in each of the four categories (men, women, boy, girls,). What does the graph suggest?

Next, treat the 2223 people aboard the Titanic as a sample. We could take the position that the titanic data in the above table constitute a population and ...

Solution Summary

The statistics and probability of the crew on the Titanic are examined.

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