JG
Jessica Gerber
Answers (2)
JG
Answered
__________ are inferred from the things people say or from their behavior.
On May 11, 2024
Attitudes
JG
Answered
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.
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.
On May 09, 2024
(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.