One of the most notable sea disasters occurred with the sinking of

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One of the most notable sea disasters occurred with the sinking of the Titanic on Monday, April 15, 1912. 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 first to be saved.

FATE OF PASSANGERS AND CREW OF THE TITANIC
MEN WOMEN BOYS GIRLS
SURVIVED 332 318 29 27
DIED 1360 104 35 18

If we examine the data we see that 19.6% of the men(332out 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, boys and 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 constitutes a population and therefore should 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 condition, but we will make that assumption for the purpose of this discussion and analysis. We can then determine whether the observed differences have statistical significant. Use one or more formal hypothesis test to investigate the claim that although some men survive while some women and children died, the rule of “women and children first” was essentially followed. Identify the hypothesis test(s) used to interpret the results by addressing the claim that when the titanic sank on its maiden voyage, the rule of “women and children first” was essentially followed.

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