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ACC544 Decision Support Tools

tag 0 Download 2 Pages / 374 Words tag 07-07-2021

Question:

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 10 hours and is believed to be normally distributed. The company proposes to collect random samples of 64 observations to monitor labour time.

  1. 1If management wishes to establish x ? 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
 (b)
Hypothesis testing
Company A has invested a great deal of time and money in occupational safety training for its employees and claims its occupational sick days are now below the national average. The national average was found to be 1.5 occupational sick days. per 100 employees with a standard deviation of 0.3 days.

Company A randomly selected 100 employees for the last year and found the sample had a mean of 1.3 occupational sick days which Company A believed supported their claim.

Using hypothesis testing with an alpha level of 0.05 and a 1-tail test, show the null and alternative hypotheses, sketch the distribution showing mean and critical region, and determine whether Company A’s belief is supported.

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