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 20 hours with a standard deviation of 9 hours and is believed to be normally distributed. The company proposes to collect random samples of 36 observations to monitor labour time.
a) If management wishes to establish x¯ control limits covering the 95% confidence interval, calculate the appropriate UCL and LCL.
b) If management wishes to use smaller samples of 9 observations calculate the control limits covering the 95% confidence interval.
c) Management is considering three alternative procedures in order to maintain tighter control over labour time:
- Sampling more frequently using 9 observations and setting confidence intervals of 80%
- Maintaining 95% confidence intervals and increasing sample size to 64 observations
- Setting 95% confidence intervals and using sample sizes of 100 observations.
Which procedure will provide the narrowest control limits? What are they?