A local planning commission is interested in finding out what proportion of its city's residents is opposed to constructing a new baseball stadium in the downtown area. A random sample of 1870 residents is obtained, and 41.2 percent of them are opposed to the stadium.
The commission is 95 percent confident that between _____ of the city's residents are opposed to constructing a new baseball stadium in the downtown area.
A) 1867.7 and 1872.3
B) 41.187 percent and 41.223 percent
C) 38.9 percent and 43.5 percent
D) 41.2 percent and 58.8 percent

Question

Quizplus · Accepted Answer

We can construct a 95% confidence interval for the true proportion of residents opposed to the stadium using the formula:
sample proportion ± z* standard error
where z* is the z-score corresponding to the desired level of confidence, and the standard error is given by:
sqrt[(sample proportion * (1 - sample proportion)) / n]
Plugging in the given values, we get:
0.412 ± 1.96 * sqrt[(0.412 * 0.588) / 1870]
Simplifying this expression, we get:
0.412 ± 0.016
Therefore, the 95% confidence interval for the true proportion of residents opposed to the stadium is:
0.396 to 0.428
This corresponds to answer choice C.

A Local Planning Commission Is Interested in Finding Out What