A large national company is considering negotiating cellular phone rates for its employees. The Human Resource department would like to estimate the proportion of its employee population who own an Apple iPhone. A random sample of size 250 is taken and 40% of the sample own an iPhone. The 95% confidence interval to estimate the population proportion is ___.
A) 0.35 to 0.45
B) 0.34 to 0.46
C) 0.37 to 0.43
D) 0.39 to 0.41
E) 0.40 to 0.42

Question

Quizplus · Accepted Answer

Using the formula for a confidence interval for a proportion with a sample size greater than 30, we get:
CI = sample proportion ± z*√(sample proportion * (1 - sample proportion) / sample size)
CI = 0.40 ± 1.96*√(0.40 * 0.60 / 250)
CI = 0.40 ± 0.07
CI = (0.34, 0.46)
Therefore, the 95% confidence interval to estimate the population proportion of Apple iPhone owners is 0.34 to 0.46. The closest choice is B.

A Large National Company Is Considering Negotiating Cellular Phone Rates