Question

how large of a sample of state employee should be taken if we want to estimate with 98% confidence the mean salary to within 2000 g

Answer 1

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

How large of a sample of state employees should be taken if we want to estimate with 98% confidence the mean salary to be within $2,000? The population standard deviation is assumed to be $10,500. z-value for 98% confidence level is 2.326.

Answer:

Sample size = n = 150

Explanation:

Recall that the margin of error is given by

`$ MoE = z \cdot ((\sigma)/(√(n) ) ) $\\\\`

Re-arranging for the sample size (n)

`$ n = ((z \cdot \sigma )/(MoE))^(2) $`

Where z is the value of z-score corresponding to the 98% confidence level.

Since we want mean salary to be within $2,000, therefore, the margin of error is 2,000.

The z-score for a 98% confidence level is 2.326

So the required sample size is

`n = ((2.326 \cdot 10,500 )/(2,000))^(2)\\\\n = (12.212)^(2)\\\\n = 149.13\\\\n = 150`

Therefore, we need to take a sample size of at least 150 state employees to estimate with 98% confidence the mean salary to be within $2,000.