A recent survey of 54,000 randomly selected U.S. adults studied the religious affiliation of Americans. The survey interviewed 645 people in Oregon. Suppose that this is a simple random sample of adult residents of Oregon. Of these 645 people, 116 said they claimed no religious identity. A 95 percent confidence interval for the proportion of all residents of Oregon who claim no religious identity is closest to:
A) 0.16 to 0.20.
B) 0.15 to 0.21.
C) 0.14 to 0.22.
D) 0.13 to 0.23.

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for a proportion:

CI = sample proportion ± z* (standard error)

where sample proportion is p̂ = 116/645 = 0.18, z* is the z-value associated with a 95% confidence level, and the standard error is:

SE = √(p̂(1-p̂)/n) = √(0.18(1-0.18)/645) ≈ 0.025

Using a standard normal distribution table, we find that the z-value associated with a 95% confidence level is 1.96.

Thus, the 95% confidence interval is:

0.18 ± 1.96(0.025) = (0.15, 0.21)

Therefore, the closest answer choice is B, 0.15 to 0.21.

A Recent Survey of 54,000 Randomly Selected U