Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches, with a standard deviation of 0.027 inches. As the machine functions over an extended number of work shifts, the standard deviation remains unchanged, but the combination of accumulated deposits and mechanical wear causes the mean diameter to “drift” away from the desired 2.500 inches. For a recent random sample of 34 tubes, the mean diameter was 2.509 inches. At the 0.01 level of significance, does the machine appear to be in need of maintenance and calibration? Determine and interpret the p-value for the test.
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