Instruction 18-3
A political pollster randomly selects a sample of 100 voters each day for eight successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favouring the incumbent candidate is too erratic.
$$\begin{array} { | c | c | }
\hline \begin{array} { c }
\text { Sample } \
\text { (Day) }
\end{array} & \begin{array} { c }
\text { Number Favouring } \
\text { Incumbent Candidate }
\end{array} \
\hline 1 & 57 \
\hline 2 & 57 \
\hline 3 & 53 \
\hline 4 & 51 \
\hline 5 & 55 \
\hline 6 & 60 \
\hline 7 & 56 \
\hline 8 & 59 \
\hline
\end{array}$$
-Referring to Instruction 18-3,what is the numerical value of the upper control limit for the p chart?
A) 0.71
B) 0.62
C) 0.89
D) 0.92

Question

Instruction 18-3
A political pollster randomly selects a sample of 100 voters each day for eight successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favouring the incumbent candidate is too erratic.
 $$\begin{array} { | c | c | } 
\hline \begin{array} { c } 
\text { Sample } \
\text { (Day) }
\end{array} & \begin{array} { c } 
\text { Number Favouring } \
\text { Incumbent Candidate }
\end{array} \
\hline 1 & 57 \
\hline 2 & 57 \
\hline 3 & 53 \
\hline 4 & 51 \
\hline 5 & 55 \
\hline 6 & 60 \
\hline 7 & 56 \
\hline 8 & 59 \
\hline
\end{array}$$
-Referring to Instruction 18-3,what is the numerical value of the upper control limit for the p chart?
A) 0.71
B) 0.62
C) 0.89
D) 0.92

Quizplus · Accepted Answer

To find the upper control limit for a p chart, we use the formula UCLp = p + 3*sqrt((p*(1-p))/n), where p is the proportion of successes (voters in favor of the incumbent) and n is the sample size (100 in this case).

We don't have any information on the proportion of voters in favor of the incumbent, so we'll assume a worst-case scenario of p=0.5 (where there is equal support for both candidates).

Using this worst-case scenario, we plug in the values to get:
UCLp = 0.5 + 3*sqrt((0.5*(1-0.5))/100) = 0.89

Therefore, the numerical value of the upper control limit for the p chart is 0.89.

The best choice is C because it is the only option that matches this calculation.

Instruction 18-3 a Political Pollster Randomly Selects a Sample of 100

Instruction 18-3
a Political Pollster Randomly Selects a Sample of 100