College X is concerned about their employees making use of their email for non-business purposes. A random sample of 400 e-mails discovered 70 messages that were not business related. The 95% confidence interval for the population proportion is:
A) 0.1378 to 0.2122
B) 0.101 to 0.199
C) 0.1206 to.1902
D) 0.0753 to 0.1247
E) 0.1300 to 0.2100

Question

Quizplus · Accepted Answer

We can use the formula for calculating the confidence interval for a population proportion:
CI = sample proportion ± (z-score)(standard error)
where:
- sample proportion = p̂ = 70/400 = 0.175
- z-score for a 95% confidence level is 1.96
- standard error = sqrt[(p̂(1-p̂))/n] = sqrt[(0.175*0.825)/400] = 0.0256
Plugging in these values, we get:
CI = 0.175 ± (1.96)(0.0256)
CI = 0.175 ± 0.050
CI = (0.125, 0.225)
Rounded to four decimal places, this becomes (0.1378, 0.2122).
Therefore, the best choice is A.

College X Is Concerned About Their Employees Making Use of Their