Historically,the average time to service a customer complaint has been 3 days and the standard deviation has been 0.50 day.Management would like to specify the control limits for an -chart with a sample size of 10 and 3 sigma limits.Suppose the next sample of 10 yielded the following result: 3.2,2.1,3.6,2.8,3.9,3.5,2.7,4.1,2.6,and 3.3.What conclusion can be drawn?
A)Assuming the process variability is in control,the process average is also in statistical control.
B)Assuming the process average is in control,the process average is out of statistical control.
C)The sample size should be increased.
D)No conclusion can be drawn because there is insufficient data.

Question

Historically,the average time to service a customer complaint has been 3 days and the standard deviation has been 0.50 day.Management would like to specify the control limits for an  -chart with a sample size of 10 and 3 sigma limits.Suppose the next sample of 10 yielded the following result: 3.2,2.1,3.6,2.8,3.9,3.5,2.7,4.1,2.6,and 3.3.What conclusion can be drawn?
A)Assuming the process variability is in control,the process average is also in statistical control. 
B)Assuming the process average is in control,the process average is out of statistical control. 
C)The sample size should be increased. 
D)No conclusion can be drawn because there is insufficient data.

Quizplus · Accepted Answer

We can calculate the control limits as follows:
Center Line = Average of the sample = (3.2+2.1+3.6+2.8+3.9+3.5+2.7+4.1+2.6+3.3)/10 = 3.2
Standard Deviation = 0.50 (given)
3 Sigma Limits = Center Line +/- 3*Standard Deviation/sqrt(sample size) = 3.2 +/- 3*0.50/sqrt(10) = 3.2 +/- 0.47
Upper Control Limit (UCL) = 3.67
Lower Control Limit (LCL) = 2.73
All the observed values are within the control limits, indicating that the process is in statistical control. Therefore, the conclusion is that assuming the process variability is in control, the process average is also in statistical control.

Historically,the Average Time to Service a Customer Complaint Has Been