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

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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.

Sample size = n = 150

Step-by-step explanation:

Recall that the margin of error is given by

Re-arranging for the sample size (n)

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

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.

(x, y)→(x − 8, y − 7)

step-by-step explanation:

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