At a Certain Manufacturing Plant, a Machine Produces Ball Bearings

At a certain manufacturing plant, a machine produces ball bearings that should have a diameter of 0.500 mm. If the machine produces ball bearings that are either too small or too large, the ball bearings must be scrapped. Every hour, a quality control manager takes a random sample of 36 ball bearings to test to see if the process is "out of control" (i.e. to test to see if the average diameter differs from 0.500 mm). Assume that the process is maintaining the desired standard deviation of 0.06 mm. The results from the latest sample follow: $$\begin{array} { l l l l l l } 0.468 & 0.521 & 0.421 & 0.476 & 0.448 & 0.346 \\0.452 & 0.513 & 0.465 & 0.395 & 0.558 & 0.526 \\0.354 & 0.474 & 0.447 & 0.405 & 0.411 & 0.453 \\0.456 & 0.477 & 0.529 & 0.440 & 0.570 & 0.319 \\0.471 & 0.480 & 0.499 & 0.446 & 0.405 & 0.557 \\0.468 & 0.521 & 0.421 & 0.476 & 0.448 & 0.346\end{array}$$ At a .01 level of significance, use Excel to test whether the process is out of control.