A random sample of 42 college graduates revealed that they worked an average of 5.5 years on the job before being promoted. The population standard deviation was 1.1 years. Using the 0.99 degree of confidence, what is the confidence interval for the population mean?
A) 5.04 and 5.96
B) 5.06 and 5.94
C) 2.67 and 8.33
D) 4.40 and 6.60

Question

Quizplus · Accepted Answer

We can use the formula:

confidence interval = sample mean ± (z-score)(standard error)

where the standard error = population standard deviation / sqrt(sample size)

First, we need to find the z-score for a 0.99 degree of confidence, which is 2.576 (using a z-table or calculator).

Next, we can plug in the values:

confidence interval = 5.5 ± (2.576)(1.1/sqrt(42))
confidence interval = 5.5 ± 0.448
confidence interval = (5.06, 5.94)

Therefore, the confidence interval for the population mean is 5.06 to 5.94, and the best choice is B.

A Random Sample of 42 College Graduates Revealed That They