Q 8.98 - Elementary Statistics

Question

Corporate Farms. The U.S. Census Bureau estimates the mean value of the land and buildings per corporate farm. Those estimates are published in the Census of Agriculture, Suppose that an estimate, $x$, is obtained and that the margin of error is $\backslash (1000$. Does this result imply that the true mean. $\mu$, is within $\backslash )1000$ of the estimate? Explain your answer.

Step-by-Step Solution

Answer

True mean can or can not lie within $\$1000$ of sample mean.

Step 1: Given Information

Margin of Error is $\$1000$ and $\stackrel{-}{x}$ is estimated.

Step 2: Explanation

At $100(1-\alpha )\%$ level of confidence, margin of error is $\$1000$.

It means that it is not necessary that true mean is within $\$1000$ of sample mean.

It can or can't lie within $\$1000$ of sample mean.

It is $100(1-\alpha )\%$ sure that true mean $\mu$ is within $\$1000$ of sample mean.