Question

Following maintenance and calibration, an extrusion machine produces aluminium 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?

Use the Critical Value Approach.

Answer 1

H0: = 2.500

Ha: 2.500

Test statistics

z = - / ( / sqrt(n) )

= 2.509 - 2.500 / ( 0.027 / sqrt(34) )

= 1.94

This is test statistics value.

Critical value at 0.01 level = -2.576 , 2.576

Since test statistics value falls in non-rejection region, we do not have sufficient evidence to reject H0.

We conclude at 0.01 level that we fail to support the claim.