Case Study: Quality Associates, Inc.
Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturing processes. In one particular application, a client gave Quality Associates a sample of 800 observations taken during a time in which that client's process was operating satisfactorily. The sample standard deviation for these data was 0.21; hence, with so much data, the population standard deviation was assumed to be 0.21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analyzing the new samples, the client could quickly learn whether the process was operating satisfactorily. When the process was not operating satisfactorily, corrective action could be taken to eliminate the problem. The design specification indicated the mean for the process should be 12. The hypothesis test suggested by Quality Associates follows.
H0: = 12
Ha: ≠ 12
Corrective action will be taken any time
H0
is rejected.
Managerial Report
Prepare a managerial report to establish process control limits for a process with a mean value of 12 at a 0.01 level of significance.
Given Data
Standard Deviation
Hypothesis Tests
Control Limits
Level of Significance
Upload Your Work
Answer (1)
Managerial ReportStandard Deviation: σ = 0.21.Hypotheses: H₀: μ = 12; Hₐ: μ ≠ 12.Significance Level: α = 0.01.Sample Size: n = 30.Standard Error: σ/√n = 0.21/√30 ≈ 0.0384.Control Limits (95% CI but at 99% α=0.01):Z = ±2.576.Margin of Error = 2.576 × 0.0384 ≈ 0.099.So, control limits: 12 ± 0.099 → [11.901, 12.099].Report: If future sample means fall outside 11.901–12.099, reject H₀ and take corrective action.
