Question

A city planner randomly selects 100 apartments in Boston, Massachusetts, to estimate the mean living area per apartment. The sample yielded x = 875 square feet with a standard deviation s = 255 square feet.

1) Calculate a 95% confidence interval for μ, the mean living area per apartment. (Keep in mind that since the sample size is large, s should be close to σ.)

Answer 1

To calculate a 95% confidence interval for the mean living area per apartment, use the formula: sample mean plus or minus the margin of error.

Step-by-step explanation:

To calculate a 95% confidence interval for the mean living area per apartment, we can use the formula:

1. Start with the sample mean, x = 875 square feet.
2. Calculate the margin of error, which is 1.96 times the standard deviation of the sample mean divided by the square root of the sample size: (1.96 * 255) / sqrt(100) = 49.98 square feet.
3. The confidence interval is the sample mean plus or minus the margin of error: 875 - 49.98 to 875 + 49.98.