Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
-95% confidence; n = 380, x = 50
A) 0.0306
B) 0.0408
C) 0.0340
D) 0.0357

Question

Quizplus · Accepted Answer

To find the margin of error, we use the formula:
E = z*sqrt(p*(1-p)/n)
where z is the z-score corresponding to the confidence level, p is the sample proportion (estimated by x/n), and n is the sample size.
For a 95% confidence level, the z-score is 1.96 (from standard normal table).
Plugging in the given values, we get:
E = 1.96*sqrt(0.1316/380)
E = 0.0340 (rounded to four decimal places)
Therefore, the best choice is C.

Assume That a Sample Is Used to Estimate a Population