Step 1 :Given that the significance level \(\alpha=0.005\) and the test is one-tailed (as we are testing \(\mu_{d}>0\)), we can use the standard normal distribution (Z-distribution) to find the critical value. The critical value is the z-score such that the area to its right under the standard normal curve is equal to \(\alpha\).
Step 2 :Using the standard normal distribution table or a calculator, we find that the critical value is approximately 2.576.
Step 3 :Final Answer: The critical value for this test is \(\boxed{2.576}\).