Question

A sample of 100 janitors in a certain school district found that the average time each janitor had worked for the school district was 8 years. Suppose we know that the standard deviation of the population is s=5 years. Construct a 95% confidence interval for the mean time of the population of janitors have spent with the school district.

A) 8±1.98
B) 8±0.82
C) 8±0.71
D) 8±1.53
E) 8±0.98

Answer 1

First, we get the standard error of the mean using
σm = σ / √N
= 5 / √100
= 0.5

Next, we subtract and add 1.96 standard deviations from the mean (since the confidence interval is 95%). So,
8 ±1.96 (0.5)
= 8 ± 0.98

The answer is
E) 8±0.98