In given Example, the information given was that 3% of a nationwide randomly selected sample of n = 883 suffered from severe allergies.
a. Determine the standard error of the sample proportion in this problem.
b. Verify that the margin of error is about 1.1% for a 95% confidence interval for the percentage that suffers from severe allergies in the population represented by this sample.
Example
In the Marist Institute allergy survey, about 3% said that they experienced "severe" allergy symptoms. The sample size is n = 883, so a conservative approximation of the margin of error is 1/√883 = .034, or 3.4%.