The U.S. Census Bureau would like to estimate the average square footage of a new single-family home with a 95% confidence interval and a margin of error within plus or minus 100 square feet. Assuming the standard deviation for the square footage of new single-family homes is 850 square feet, the required sample size is ----------.
A)203
B)278
C)232
D)295

Question

Quizplus · Accepted Answer

To calculate the required sample size for estimating a population mean with a specific confidence level and margin of error, the formula is: $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $n$ is the sample size, $Z$ is the Z-score corresponding to the desired confidence level, $\sigma$ is the population standard deviation, and $E$ is the margin of error. For a 95% confidence interval, the Z-score is approximately 1.96. Given $\sigma = 850$ square feet and $E = 100$ square feet, substituting these values into the formula gives: $n = \left(\frac{1.96 \cdot 850}{100}\right)^2 \approx 278$. Therefore, a sample size of approximately 278 is required.

The US Census Bureau Would Like to Estimate the Average Square