A random sample of 85 group leaders, supervisors, and similar personnel revealed that on the average a person spent 6.5 years on the job before being promoted. The standard deviation of the population was 1.7 years. Find the 95% 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

Since we are trying to find the confidence interval for population mean, we can use the formula:

Confidence Interval = sample mean ± (critical value) x (standard error)

First, we need to find the critical value at 95% confidence level. Since the sample size is greater than 30, we can use the Z-score table. At 95% confidence level, the Z-score is 1.96.

Next, we need to calculate the standard error:

Standard Error = standard deviation / square root of sample size
Standard Error = 1.7 / √85
Standard Error = 0.184

Now we can plug in the values to get the confidence interval:

Confidence Interval = 6.5 ± 1.96 x 0.184
Confidence Interval = 6.14 and 6.86

Therefore, the best choice is C) 6.14 and 6.86 with a 95% confidence level.

A Random Sample of 85 Group Leaders, Supervisors, and Similar