Asked by Jordan Jeyachandran on May 05, 2024
Verified
A department chair wants to monitor the percentage of failing students in classes in her department. Each class had an enrollment of 50 students last spring. The number of failing students in the 10 classes offered that term were 1, 4, 2, 0, 0, 0, 0, 0, 0, and 3, respectively. Compute the control limits for a p-chart at the 95% confidence level. Is the process in control?
Control Limits
Statistical boundaries set in process control that indicate the maximum and minimum values within which a process should operate to produce acceptable outcomes.
Failing Students
Students who are unable to meet the academic standards or pass the assessments of their educational program.
- Ascertain and explicate the control limits and capabilities of processes within diverse control chart formats (e.g., X-bar, R-chart, p-chart, and c-chart).
- Evaluate sample information to decide if a process adheres to statistical control.
- Distinguish between variations arising from natural processes and those attributable to specific causes.
Verified Answer
RS
Rachel SolomonsMay 07, 2024
Final Answer :
From Table S6.2 in the text, the z-value = 1.96.
The mean p-bar = [1 + 4 + 2 + 0 + 0 + 0 + 0 + 0 + 0 + 3]/(50 × 10) = 0.02.
σp= 0.02(1−0.02)50\sqrt { \frac { 0.02 ( 1 - 0.02 ) } { 50 } }500.02(1−0.02) 0.0198
UCLp = 0.02 + 1.96(.0198) = 0.0589
LCLp = 0.02 - 1.96(.0198) = -0.0189 (or 0)
Since the percent defects in classes 2 and 10 both exceeded 5.89%, the percentage of failing students is not in statistical control. The department chair should investigate.
The mean p-bar = [1 + 4 + 2 + 0 + 0 + 0 + 0 + 0 + 0 + 3]/(50 × 10) = 0.02.
σp= 0.02(1−0.02)50\sqrt { \frac { 0.02 ( 1 - 0.02 ) } { 50 } }500.02(1−0.02) 0.0198
UCLp = 0.02 + 1.96(.0198) = 0.0589
LCLp = 0.02 - 1.96(.0198) = -0.0189 (or 0)
Since the percent defects in classes 2 and 10 both exceeded 5.89%, the percentage of failing students is not in statistical control. The department chair should investigate.
Learning Objectives
- Ascertain and explicate the control limits and capabilities of processes within diverse control chart formats (e.g., X-bar, R-chart, p-chart, and c-chart).
- Evaluate sample information to decide if a process adheres to statistical control.
- Distinguish between variations arising from natural processes and those attributable to specific causes.