A researcher is interested in estimating the average salary of police officers in a large city. She wants to be 99% confident that her estimate is correct. If the standard deviation is $1050, how large a sample is needed to get the desired information and to be accurate within $200?

Question

Mathematics

Joy Greer

25 March, 12:49

A researcher is interested in estimating the average salary of police officers in a large city. She wants to be 99% confident that her estimate is correct. If the standard deviation is $1050, how large a sample is needed to get the desired information and to be accurate within $200?

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Answers (1)

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Tiara · Answer 1

Given:

σ = $1050, ppulatin standard deviation

99% confidence interval

Accuracy = + / - $200

The accuracy is given by

z * (σ/√n)

where

z * = 2.576 for 99% confidence level (from tables)

n = sample size

Therefore

2.576 (1050/√n) = 200

√n = (2.576*1050) / 200 = 13.524

n = 182.9

Answer: The sample size is 183