Question

Workers and​ senior-level bosses were asked if it was seriously unethical to monitor employee​ e-mail. The results are summarized in the table to the right. Use a 0.05 significance level to test the claim that the response is independent of whether the subject is a worker or a boss.         Yes   No Workers   192   250 Bosses 42   85 Assuming independence between the two​ variables, find the expected frequency for each cell of the table. Table of expected frequencies Yes No Workers Bosses

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=0.05 , the number of degrees of freedom is df=(2−1)×(2−1)=1, so then the rejection region for this test is R={χ2:χ2>3.841}.

Test Statistics

The Chi-Squared statistic is computed as follows:

The decision about the null hypothesis

Since it is observed that χ2=4.38>χc2​=3.841, 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 0.05 significance level.

The corresponding p-value for the test is p=Pr(χ12​>4.38)=0.0364.

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