College X is concerned about their employees making use of their email for non-business purposes. A random sample of 400 e-mails discovered 40 messages that were not business related. The 95% confidence interval for the population proportion is:
A) 0.199 to 0.201
B) 0.101 to 0.199
C) 0.07060 to0.12940
D) 0.0753 to 0.1247
E) 0.0700 to 0.1000

Question

Quizplus · Accepted Answer

The formula for the confidence interval for a population proportion is:sample proportion +/- margin of errorwhere the margin of error is:z * sqrt((sample proportion * (1 - sample proportion)) / sample size)where z is the z-score corresponding to the desired confidence level.For a 95% confidence level, z = 1.96.Plugging in the values we have:0.1 +/- 1.96 * sqrt((0.1 * (1 - 0.1)) / 400)= 0.1 +/- 1.96 * sqrt((0.1 * 0.9) / 400)= 0.1 +/- 1.96 * sqrt(0.00225)= 0.1 +/- 1.96 * 0.0474= 0.1 +/- 0.0929Therefore, the 95% confidence interval is (0.07060, 0.12940).

College X Is Concerned About Their Employees Making Use of Their