Question

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 () ()

Answer 1

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

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!