A company wishes to set control limits for monitoring the direct labour time to produce an important product. Over the past the mean time has been 30 hours with a standard deviation of 10 hours and is believed to be normally distributed. The company proposes to collect random samples of 64 observations to monitor labour time.

1. If management wishes to establish x-bar control limits covering the 95% confidence interval, calculate the appropriate UCL and LCL.
2. If management wishes to use smaller samples of 16 observations; calculate the control limits covering the 95% confidence interval.
3. Management is considering three alternative procedures in order to maintain tighter control over labour time:

• Sampling more frequently using 16 observations and setting confidence intervals of 90%
• Maintaining 95% confidence intervals and increasing sample size to 64 observations
• Setting 95% confidence intervals and using sample sizes of 36 observations.

Calculate the control limits for each of the 3 alternatives.

Which procedure will provide the narrowest control limits? What are they?