Question: A machine produces 3-inch nails. A sample of 10 nails was selected and the lengths determined. The results are as follows:

2.89 2.95 3.00 3.05 2.99 2.96 3.10 3.06 3.00 3.12

Use these results to test H₀: m = 3 and H_a: m ¹ 3 at a = 0.01. Give the critical region, the computed test statistic, and the conclusion.