In: Statistics and Probability
4. Did the class of service play a role in the survival of passengers in the infamous Titanic disaster? The data shown represents the survival status of passengers by class of service.
Survived |
Did not survive |
|
First class |
203 |
122 |
Second class |
118 |
167 |
Third class |
178 |
528 |
Is class of service independent of survival rate? Use the ? = 0.10 level of significance. (Show all six steps for hypothesis testing.)
Show your work for calculating the test statistic by writing terms ?, ?, (?−?)2 for each cell. ?
Survived |
Did not survive |
|
First class |
203 (123.23) (51.64) |
122 () () |
Second class |
118 () () |
167 () () |
Third class |
178 () () |
Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
H0: The two variables are independent
Ha: The two variables are dependent
This corresponds to a Chi-Square test of independence.
Rejection Region
Based on the information provided, the significance level is α=0.10 , the number of degrees of freedom is df=(3−1)×(2−1)=2, so then the rejection region for this test is R={χ2:χ2>4.605}.
Test Statistics
The Chi-Squared statistic is computed as follows:
Decision about the null hypothesis
Since it is observed that , it is then concluded that the null hypothesis is rejected.
Conclusion
It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.10 significance level.
The corresponding p-value for the test is
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