The "unsinkable" luxury liner Titanic collided with an iceberg on her maiden voyage in 1912 and sank with great loss of life. On board were 1317 passengers, some of whom had paid much higher fare than others for the voyage. A not very subtle sub-text in the most recent Titanic movie was the notion that the first class passengers survived at a higher rate than other passengers.

On Titanic, there were 324 first class passengers of whom 203 survived the sinking. Among the 712 third class passengers, 178 survived. Let T1 denote the survival rate of first class passengers and T2 denote the survival rate of third class passengers on any cruise liner if the cruise liner is capsized. Using a 5% significance level, test whether the survival rate for first class passengers was greater than that for third class passengers (round to two decimal places). Write down the five steps of hypothesis testing and use the critical value approach for step 5.

Design of Hypothesis Testing

There are five steps in the process of hypothesis testing:
1 Formulate the hypotheses: set up the null (Ho) and alternative (Ha) hypotheses for the question at hand.
2 Specify the level of significance, a.
3 Determine the appropriate estimator, test statistic and its sampling distribution.
4 Compute the value of the test statistic from the sample.
5 Make a decision (of whether or not to reject the null) using one of the following approaches:
          1 the p-value approach;
          2 the critical value approach.

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