A county with a large population need to know what the average income is for tax purposes. A simple random sample of 1000 household reveals the following information. The average household income for the sample is $21,000. The median income of the sample is $17,000. The SD of the sample is $10,000, Q1 = $11,000 and Q3 = $24,000.
ConfIntervalAns
The confidence interval for the average household income in the county can be calculated using the given information.
The formula to calculate the confidence interval is:
CI = X̄ ± Z * (SD / √n)
Where:
CI = Confidence Interval
X̄ = Sample mean
Z = z-score (corresponding to the desired level of confidence)
SD = Sample standard deviation
n = Sample size
The value of Z will depend on the desired level of confidence. Assuming a 95% confidence level, the z-score for a 95% confidence level is approximately 1.96.
Plugging in the values into the formula, we have:
CI = $21,000 ± 1.96 * ($10,000 / √1000)
Simplifying, we get:
CI = $21,000 ± 1.96 * $316.23
CI = $21,000 ± $619.65
Thus, the confidence interval for the average household income in the county is:
$20,380.35 to $21,619.65