Question

The number of square feet per house are normally distributed with a population standard deviation of 137 square feet and an unknown population mean. A random sample of 19 houses is taken and results in a sample mean of 1350 square feet. Find the margin of error for a 80% confidence interval for the population mean. z0.10z0.10z0.05z0.05z0.025z0.025z0.01z0.01z0.005z0.005 1.2821.6451.9602.3262.576 You may use a calculator or the common z values above. Round the final answer to two decimal places.

Answer 1

Answer:

The MOE for 80% confidence interval for μ is 5.59.

Step-by-step explanation:

The random variable X is defined as the number of square feet per house.

The random variable X is Normally distributed with mean μ and standard deviation σ = 137.

The margin of error for a (1 - α) % confidence interval for population mean is:

$MOE=z_{\alpha /2}\times\frac{\sigma}{\sqrt{n}}$

Given:

n = 19

σ = 137

$z_{\alpha /2}=z_{0.20/2}=z_{0.10}=1.282$

Compute MOE for 80% confidence interval for μ as follows:

$MOE=1.282\times\frac{137}{\sqrt{19}}=1.282\times4.36=5.58952\approx5.59$

Thus, the MOE for 80% confidence interval for μ is 5.59.