College X is concerned about their employees making use of their email for non-business purposes. A random sample of 400 e-mails discovered 80 messages that were not business related. The 90% confidence interval for the population proportion is:
A) 0.167 to 0.233
B) 0.161 to 0.239
C) 0.148 to 0.252
D) 0.186 to 0.254
E) 0.179 to 0.261

Question

Quizplus · Accepted Answer

The proportion of non-business related emails is 80/400 = 0.2. For a 90% confidence interval, the z-score is approximately 1.645. The standard error (SE) is calculated using the formula SE = sqrt[(p(1-p))/n], where p is the sample proportion and n is the sample size. Substituting the values, SE = sqrt[(0.2*0.8)/400] = 0.02. The margin of error (ME) is z*SE = 1.645*0.02 = 0.0329. Therefore, the confidence interval is 0.2 ± 0.0329, which is approximately 0.167 to 0.233.

College X Is Concerned About Their Employees Making Use of Their