Asked by Megan kibby on Apr 26, 2024
Verified
A retail store manager is trying to improve and control the rate at which cashiers sign customers up
for store credit cards. Suppose the manager takes 10 samples, each with 100 observations. P-bar
is found to be .05, and the manager does not want a lower limit below .0064. What z-value would
this imply, and how confident can he be that the true lower limit is greater than or equal to .0064?
P-bar
The average proportion of units in a sample that exhibit a particular characteristic, used in quality control processes.
Z-value
A statistical measure representing the number of standard deviations from the mean a data point is.
Lower Limit
The lowest value in a set of data, or the minimum value that a certain variable, function, or sequence can assume.
- Undertake the computation and explanation of control limits and the capabilities of processes within different control chart categories (e.g., X-bar, R-chart, p-chart, and c-chart).
- Apply the rules of three-sigma for the purpose of determining process control.
Verified Answer
SU
Steven UnderwoodApr 26, 2024
Final Answer :
Sigma-p = sqrt ( .05∗(1 - .05)/100) = .0217945. Using the equation that LCL = p-bar-z∗sigma-p gives .0064 = .05 - z∗(.0217945). Solving gives z = 2. Using Table S6.2 in the text shows that for z = 2 the manager can be 95.45% confident.
Learning Objectives
- Undertake the computation and explanation of control limits and the capabilities of processes within different control chart categories (e.g., X-bar, R-chart, p-chart, and c-chart).
- Apply the rules of three-sigma for the purpose of determining process control.