A November 2015 poll of size n = 1021 had a sample proportion = 0.86 disapproving of Congress. If this is regarded as a simple random sample, then a 95 percent confidence interval for the proportion p of all adults who disapprove of Congress is closest to:
A) 0.86 ± 0.000231.
B) 0.86 ± 0.0105.
C) 0.86 ± 0.021.
D) 0.86 ± 0.03.

Question

Quizplus · Accepted Answer

Since we are looking for a 95% confidence interval for the population proportion based on a sample proportion, we can use the formula:

sample proportion ± (critical value)*(standard error)

The critical value can be found using a normal distribution table or calculator, and for a 95% confidence interval with a two-tailed test, it is approximately 1.96.

The standard error can be calculated using:

sqrt[(sample proportion)*(1 - sample proportion)/n]

Plugging in the given values:

sample proportion = 0.86 
n = 1021

standard error = sqrt[(0.86)*(1 - 0.86)/1021] ≈ 0.013

Therefore, the 95% confidence interval is:

0.86 ± 1.96*0.013 ≈ 0.86 ± 0.025

The closest answer choice is C, 0.86 ± 0.021.

A November 2015 Poll of Size N = 1021 Had