Discussion:
Q: A lathe is set to cut steel bars into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is equal to 6 centimeters. A sample of 25 bars is selected randomly, and the lengths are measured. It is determined that the average length of the bars in the sample is 6.1 centimeters with a standard deviation of 0.2 centimeters. At 95% confidence, test to determine whether or not the lathe is in perfect adjustment.