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6. A random sample of 80 federal government workers found that the average annual salary for...

6. A random sample of 80 federal government workers found that the average annual salary for federal government employees in Iowa was $51,340 during 2019. Assuming the population standard deviation was σ = $5000 and that we want to use a 99% confidence interval to answer the following questions. (a) What is the margin of error? (b) What is the confidence interval for the average annual salary for federal employees?

Question 1 margin of error

Question 2 confidence interval for average annual salary for federal employees

Math   Statistics-And-Probability   
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Answer #1

The Z critical at = 0.01 is 2.576

(a) ME = Z critical * / Sqrt(n) = 2.576 * 5000 / sqrt(80) = 1440.08

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(c) The Confidence interval is given by

The Lower Limit = 51.340 - 1140.08 = 49899.92

The Upper Limit = 51340 + 1140.08 = 52780.08

The Confidence interval is (49899.92, 52780.08)

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If rounded to the nearest integer is required, then ME = 1440, and the CI will be (48900, 52780)

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