Step 1 :Given values are right-tailed test, level of significance \(\alpha=0.005\), and sample size \(n=20\).
Step 2 :Calculate the degrees of freedom as \(df = n - 1 = 20 - 1 = 19\).
Step 3 :Find the critical value using the t-distribution table. The critical value is the t-value such that the area to its right under the t-distribution curve is equal to the level of significance \(\alpha\).
Step 4 :Using the t-distribution table, the critical value is approximately 2.861.
Step 5 :The rejection region for a right-tailed test is all values greater than the critical value. So, in this case, the rejection region is all t-values greater than 2.861.
Step 6 :Final Answer: The critical value is \(\boxed{2.861}\). The rejection region is \(t>\boxed{2.861}\).