James Desreumaux, VP of Human Resources of Maritime Boat Manufacturing (MBM), is reviewing the employee training programs of MBM factories.His staff randomly selected personnel files for 100 workers in New Brunswick and determined that their mean training time was 25 hours.Assume that the population standard deviation is 5 hours.The 95% confidence interval for the population mean of training times is ___.
A)15.20 to 34.80
B)24.18 to 25.82
C)24.02 to 25.98
D)16.78 to 33.23
E)23.32 to 35.46

Question

Quizplus · Accepted Answer

Since the sample size is greater than 30 and we know the population standard deviation, we can use a z-test. The z-score for a 95% confidence level is 1.96. 
The margin of error can be calculated as:
margin of error = z-score * (standard deviation / square root of sample size)
margin of error = 1.96 * (5 / square root of 100) = 1
Therefore, the 95% confidence interval for the population mean is:
sample mean ± margin of error
25 ± 1 = (24, 26)
So the answer is C) 24.02 to 25.98.