A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 12 kilograms. To test his claim, 50 pieces of each type of thread are tested under similar conditions. Type A thread had an average tensile strength of 86.7 kilograms with known standard deviation of σ A = 6.28 kilograms, while type B thread had an average tensile strength of 77.8 kilograms with known standard deviation of σ B = 5.61 kilograms. Test the manufacturer's claim at α = 0.05.