TABLE 17-2
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.
-Referring to Table 17-2, what is the numerical value of the lower control limit for the p chart?
A) 0.37
B) 0.41
C) 0.50
D) 0.71

Question

TABLE 17-2
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. 
-Referring to Table 17-2, what is the numerical value of the lower control limit for the p chart?
A) 0.37 
B) 0.41 
C) 0.50 
D) 0.71

Quizplus · Accepted Answer

To calculate the lower control limit for a p chart, we use the formula:

LCL = p - 3√(p(1-p)/n)

where p is the overall proportion of votes favoring the incumbent, and n is the sample size (100).

From Table 17-2, we see that the overall proportion of votes favoring the incumbent is 353/800, or 0.44125. Plugging this value into the formula, we get:

LCL = 0.44125 - 3√(0.44125(1-0.44125)/100) ≈ 0.408

Therefore, the numerical value of the lower control limit for the p chart is 0.408, which corresponds to choice (B).

TABLE 17-2 A Political Pollster Randomly Selects a Sample of 100 Voters