To estimate $\mu$,the mean salary of full professors at American colleges and universities,you obtain the salaries of a random sample of 400 full professors.The sample mean is $73,220 and the sample standard deviation is $4400.What is a 99% confidence interval for the mean $\mu$?
A)73,220 ± 28
B)73,220 ± 433
C)73,220 ± 569
D)73,220 ± 4400

Question

Quizplus · Accepted Answer

To calculate the confidence interval, we can use the formula:
CI = x̄ ± z* (σ/√n)
where x̄ is the sample mean, σ is the sample standard deviation, n is the sample size, and z* is the z-score corresponding to the desired confidence level.

For a 99% confidence level, the z* value is 2.576. 
Plugging in the values, we get:
CI = 73,220 ± 2.576 * (4400/√400)
CI = 73,220 ± 569

Therefore, the best choice is option C, which is the closest to the calculated confidence interval.

To Estimate μ\muμ ,The Mean Salary of Full Professors at American Colleges and American

To Estimate $\mu$ ,The Mean Salary of Full Professors at American Colleges and American