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.
In this sample, the margin of error is
A)770.
B) 2.3 percent.
C) 41.2 percent.
D) 0.023 percent.

Question

Quizplus · Accepted Answer

The margin of error for a proportion can be calculated using the formula: 
Margin of error = z*(sqrt(p*(1-p)/n))
where z is the critical value from the standard normal distribution corresponding to the level of confidence, p is the sample proportion, and n is the sample size. Assuming a 95% level of confidence (corresponding to a z-value of 1.96), we can plug in the values from the problem: 
Margin of error = 1.96*(sqrt(0.412*(1-0.412)/1870)) = 0.023 or 2.3%
Therefore, the best choice is B, which gives the correct margin of error as a percentage. A represents an incorrect calculation (770 is not a reasonable margin of error), C is not a valid option as it simply repeats the sample proportion, and D gives the margin of error as a decimal instead of a percentage.

A Local Planning Commission Is Interested in Finding Out What