A firm having 4000 employees took a random sample of 25 in order to estimate their average annual state tax payment with 99% confidence. If the results were X = $640 and s = $20, what is the best interval estimation?
99% = mean ± 2.575 SEm
SEm = SD/√n
67
To find the best interval estimation for estimating the average annual state tax payment with 99% confidence, we can use the formula for the confidence interval.
The formula for the confidence interval is:
CI = X ± Z * (s / √n)
Where:
- CI represents the Confidence Interval
- X is the sample mean
- Z is the Z-score corresponding to the desired confidence level
- s is the standard deviation of the sample
- n is the sample size
In this case, X = $640 (sample mean), s = $20 (standard deviation of the sample), and n = 25 (sample size).
To find the Z-score for a 99% confidence level, we need to look up the value from the Z-table or use a calculator. The Z-score for a 99% confidence level (two-tailed test) is approximately 2.576.
Plugging the values into the formula:
CI = $640 ± 2.576 * ($20 / √25)
Calculating the values within the parentheses:
CI = $640 ± 2.576 * ($20 / 5)
CI = $640 ± 2.576 * $4
CI = $640 ± $10.304
Thus, the best interval estimation for the average annual state tax payment with 99% confidence is:
$640 - $10.304 ≤ μ ≤ $640 + $10.304
$629.696 ≤ μ ≤ $650.304
So the best interval estimation is $629.696 to $650.304.