Chapter 8, Problem 1CR

Terminology Answer true or false. The margin of error when using $\bar{x}$ as a point estmate for $\mu \text{ is }\bar{x}-\mu$.

To determine

Whether the statement “Themargin of error when using $\overline{x}$ as a point of estimate for $\mu$ is $\overline{x}-\mu$” is true or false.

Answer to Problem 1CR

Solution: The statement “The margin of error when using $\overline{x}$ as a point of estimate for $\mu$ is $\overline{x}-\mu$” is false.

Explanation of Solution

In most of the practical problems, $\mu$ is unknown, so the margin of error is also unknown. We can compute error tolerance E, which serves as a bound on the margin of error. The point estimate $\overline{x}$ differs from the population mean $\mu$ by a Maximal margin of errorat c % level of confidence.

The margin of error when using $\overline{x}$ as a point of estimate for $\mu$ is $|\overline{x}-\mu |$.