A machine is designed to produce ball bearings having a mean diameter of 0.574 centimeter with a standard deviation of 0.008 centimeter. To determine whether the machine is in proper working order, a sample of six ball bearings is taken every hour, and the mean diameter of each sample is recorded. (Note that each sample consists of six observations.)
a. Design a decision rule using the mean diameter of the hourly samples so that you can be 95% confident that the machine is conforming to the required design standards for mean diameter of the manufactured ball bearings.
b. The following table presents the mean diameter of the hourly samples for the day shift of one given day. Are there any conclusions that can be inferred from this data?
Time of Sample
Mean Diameter of Sample
1000 0.576
1100 - 1300 Machine down for retooling
1400 0.561