Asked by Albernisha Jones on May 05, 2024
Verified
A small, independent amusement park collects data on the number of cars with out-of-state license plates. The sample size is fixed at n = 25 each day. Data from the previous 10 days indicate the following number of out-of-state license plates:
Day Out-of-state Plates 1624354758637485931011\begin{array} { | c | c | } \hline \text { Day } & \begin{array} { c } \text { Out-of-state } \\\text { Plates }\end{array} \\\hline 1 & 6 \\\hline 2 & 4 \\\hline 3 & 5 \\\hline 4 & 7 \\\hline 5 & 8 \\\hline 6 & 3 \\\hline 7 & 4 \\\hline 8 & 5 \\\hline 9 & 3 \\\hline 10 & 11 \\\hline\end{array} Day 12345678910 Out-of-state Plates 64578345311 (a) Calculate the overall proportion of "tourists" (cars with out-of-state plates) and the standard deviation of proportions.
(b) Using ± 3σ limits, calculate the LCL and UCL for these data.
(c) Is the process under control? Explain.
Proportion
is a mathematical concept that denotes a part, share, or number considered in comparative relation to a whole.
Standard Deviation
A measure of the amount of variation or dispersion of a set of values, indicating how much the values in a data set deviate from the mean.
Control Limits
Control limits are the boundaries set in statistical process control that indicate the acceptable range of variation for a process, distinguishing between common and special causes of variation.
- Implement calculation and interpretation techniques for understanding control limits and process capabilities across distinct control chart types like X-bar, R-chart, p-chart, and c-chart.
- Study sample data to figure out if a process is governed by statistical control.
- Differentiate between natural process variations and variations due to assignable causes.
Verified Answer
JG
Jessica GerberMay 09, 2024
Final Answer :
(a) p-bar is 56/250 = 0.224; the standard deviation of proportions is the square root of
.224 × .776 / 25 = 0.0834
(b) UCL = .224 + 3 × 0.834 = .4742; LCL = .224 -3 × .0834 which is negative, so the LCL = 0
(c) The largest percentage of tourists (day 10) is 11/25 = .44, which is still below the UCL. Thus, all the points are within the control limits, so the process is under control.
.224 × .776 / 25 = 0.0834
(b) UCL = .224 + 3 × 0.834 = .4742; LCL = .224 -3 × .0834 which is negative, so the LCL = 0
(c) The largest percentage of tourists (day 10) is 11/25 = .44, which is still below the UCL. Thus, all the points are within the control limits, so the process is under control.
Learning Objectives
- Implement calculation and interpretation techniques for understanding control limits and process capabilities across distinct control chart types like X-bar, R-chart, p-chart, and c-chart.
- Study sample data to figure out if a process is governed by statistical control.
- Differentiate between natural process variations and variations due to assignable causes.