SCENARIO 15-2
A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent.The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic. $$\begin{array} { c c }
\begin{array} { c }
\text { Sample } \
\text { (Day) }
\end{array} & \begin{array} { c }
\text { Number Favoring } \
\text { IncumbentCandidate }
\end{array} \
\hline 1 & 57 \
2 & 57 \
3 & 53 \
4 & 51 \
5 & 55 \
6 & 60 \
7 & 56 \
8 & 59
\end{array}$$
-Referring to SCENARIO 15-2, what is the numerical value of the lower control limit for the pchart?
A)0.37
B)0.41
C)0.50
D)0.71

Question

SCENARIO 15-2
A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent.The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic. $$\begin{array} { c c } 
\begin{array} { c } 
\text { Sample } \
\text { (Day) }
\end{array} & \begin{array} { c } 
\text { Number Favoring } \
\text { IncumbentCandidate }
\end{array} \
\hline 1 & 57 \
2 & 57 \
3 & 53 \
4 & 51 \
5 & 55 \
6 & 60 \
7 & 56 \
8 & 59
\end{array}$$
-Referring to SCENARIO 15-2, what is the numerical value of the lower control limit for the pchart?
A)0.37
B)0.41
C)0.50
D)0.71

Quizplus · Accepted Answer

The lower control limit (LCL) for a p-chart is calculated using the formula: $$LCL = \bar{p} - Z\sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$$ where $\bar{p}$ is the average proportion, $Z$ is the Z-value from the standard normal distribution (commonly 3 for control charts), and $n$ is the sample size. First, calculate the average proportion $\bar{p}$: $$\bar{p} = \frac{57+57+53+51+55+60+56+59}{100*8} = \frac{448}{800} = 0.56$$ Then, assuming a Z-value of 3 (common for control charts), and given $n = 100$, the LCL calculation is: $$LCL = 0.56 - 3\sqrt{\frac{0.56(1-0.56)}{100}} = 0.56 - 3\sqrt{\frac{0.56*0.44}{100}} = 0.56 - 3\sqrt{0.002464} = 0.56 - 3(0.0496) = 0.56 - 0.1488 = 0.4112$$ Rounding to two decimal places, the LCL is approximately 0.41.

SCENARIO 15-2 a Political Pollster Randomly Selects a Sample of 100

SCENARIO 15-2
a Political Pollster Randomly Selects a Sample of 100