A random sample of 85 supervisors revealed that they worked an average of 6.5 years before being promoted. The population standard deviation was 1.7 years. Using the 0.95 degree of confidence,what is the confidence interval for the population mean?
A)6.99 and 7.99
B)4.15 and 7.15
C)6.14 and 6.86
D)6.49 and 7.49

Question

Quizplus · Accepted Answer

We can use the formula:

CI = X̄ ± Z* (σ/√n)

where X̄ = sample mean = 6.5 
Z = z-score for 0.95 degree of confidence = 1.96 
σ = population standard deviation = 1.7 
n = sample size = 85

Substituting values, we get:

CI = 6.5 ± 1.96 * (1.7/√85) 
CI = 6.5 ± 0.36

Hence, the confidence interval is (6.14, 6.86) 
Therefore, the best choice is (C) 6.14 and 6.86.

A Random Sample of 85 Supervisors Revealed That They Worked