Step 1 :Step # 1: The null hypothesis $H_{0}$ is that the population proportion is equal to $12.9 \%$ ($p = 0.129$), and the alternative hypothesis $H_{1}$ is that the population proportion is greater than $12.9 \%$ ($p > 0.129$). The claim is that the proportion of union members is greater than $12.9 \%$.
Step 2 :Step # 2: This is a one-tailed Z test for population proportion. The critical value for a one-tailed test with a significance level of 0.01 is approximately 2.33.
Step 3 :Step # 3: The sample proportion $\hat{p}$ is calculated as $75 / 500 = 0.15$. The test statistic is calculated as $(\hat{p} - p) / \sqrt{(p * (1 - p)) / n} = 1.40$.
Step 4 :Step # 4: Since the test statistic (1.40) is less than the critical value (2.33), we do not reject the null hypothesis.
Step 5 :Step # 5: There is not sufficient evidence at the 0.01 level of significance to conclude that the proportion of union members is greater than $12.9 \%$. Therefore, the final answer is \(\boxed{\text{There is not sufficient evidence at the 0.01 level of significance to conclude that the proportion of union members is greater than 12.9\%.}}\)