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 99% 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

To find the confidence interval, we need to use the formula:
CI = p_hat ± z_crit∗(sqrt((p_hat*(1-p_hat))/n))
where:
- p_hat is the sample proportion of non-business emails (80/400 = 0.2)
- z_crit is the critical z-value for a 99% confidence level (2.576, using a z-table or calculator)
- n is the sample size (400)

Plugging in the values, we get:
CI = 0.2 ± 2.576∗(sqrt((0.2*(1-0.2))/400))
CI = 0.2 ± 0.044
CI = (0.156, 0.244)

Therefore, the 99% confidence interval for the population proportion is 0.148 to 0.252, which is closest to choice C.

College X Is Concerned About Their Employees Making Use of Their