Question

Results from a civil servant exam are shown in the table to the right. Is there sufficient evidence to support the claim that the results from the test are​ discriminatory? Use a 0.01 significance level.

Passed Failed

White candidates 15 13

Minority candidates 9 22

Answer 1

We would use a chi square test of independence here to check whether the results are discriminatory or not.

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0​: The two variables are independent i.e. the results are not discriminatory

Ha​: The two variables are dependent i.e. the results are discriminatory

This corresponds to a Chi-Square test of independence.

Rejection Region

Based on the information provided, the significance level is α=0.01 , 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>6.635}.

Test Statistics

The Chi-Squared statistic is computed as follows:

Decision about the null hypothesis

Since it is observed that χ2=3.671≤χc2​=6.635, it is then concluded that the null hypothesis is not rejected.

Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is NOT enough evidence to claim that the two variables are dependent, at the 0.01 significance level. Hence the results are not discriminatory.

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