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 X- 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) The sample size should be increased.
B) Assuming the process variability is in control, the process average is also in statistical control.
C) Assuming the process average is in control, the process average is out of statistical control.
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 X- 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) The sample size should be increased.
B) Assuming the process variability is in control, the process average is also in statistical control.
C) Assuming the process average is in control, the process average is out of statistical control.
D) No conclusion can be drawn because there is insufficient data.

Quizplus · Accepted Answer

The sample mean is 3.18 and the sample standard deviation is 0.63. The control limits are UCL = 3 + 3 * 0.50 / sqrt(10) = 3.75 and LCL = 3 - 3 * 0.50 / sqrt(10) = 2.25. Since the sample mean is within the control limits, we can conclude that the process average is in statistical control.

Historically, the Average Time to Service a Customer Complaint Has