Final answer:
It is false that a process is in statistical control merely by being between the UCL and LCL; there should also be no non-random patterns within the limits. The z-score of 1.96 is associated with a CL of 0.95 and α of 0.05, splitting the tails' area equally.
Step-by-step explanation:
The statement that a process is in a state of statistical control if an observation is below the Upper Control Limit (UCL) and the Lower Control Limit (LCL) is false. In the context of control charts used in statistical process control, being between the UCL and LCL is a necessary, but not sufficient condition for statistical control. The process must also not show non-random patterns or trends within the control limits.
The confidence level (CL) is concerned with the area under the standard normal distribution curve. The formula CL = 1 - α represents the central area, with α being the remaining area split between the two tails of the curve. For a given CL, such as 0.95, the α is 0.05 and each tail holds an area of 0.025. The z-score that corresponds to the upper tail boundary, Z α0.025, is commonly found using a z-table or statistical software, which would yield a value of approximately 1.96. This score indicates the number of standard deviations a value is from the mean.