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 0.05 significance level.

	passed	failed
white candidates	20	15
minority candidates	9	26

Answer 1

For sample 1, White candidates we have that the sample size is N1​=35, the number of favorable cases is X1​=20, so then the sample proportion is

For sample 2, for minority candidates we have that the sample size is N2​=35, the number of favorable cases is X2​=9, so then the sample proportion is

The value of the pooled proportion is computed as

Also, the given significance level is α=0.05.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: p_1 = p_2

Ha: p_1 p_2​

This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is z_c = 1.96

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that |z| = 2.669 > z_c = 1.96 , it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0076 , and since p = 0.0076 <0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion p_1​ is different than p_2 at the 0.05 significance level.