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

Question

Baby Bird

Mathematics

8 September, 23:10

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

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Answers (1)

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Cory Bright · 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