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A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength...

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 σA = 6.28 kilograms, while type B thread had an average tensile strength of 77.8 kilograms with known standard deviation of σB = 5.61 kilograms. Test the manufacturer's claim at α= 0.05.

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