Chapter 7.1, Problem 20E

(a)

To determine

The explanation about what it means to say that $\overline{x}$ is an unbiased estimator of $\mu$ .

Answer to Problem 20E

The statement means that the average of all values of $\overline{x}$ and the value of $\mu$ are equal.

Explanation of Solution

Here, if the average of all possible values of $\overline{x}$ and $\mu$ are equal (or extremely close to $\mu$ ); then $\overline{x}$ is an unbiased estimator of $\mu$ .

Hence, the statement means that the average of all values of $\overline{x}$ and the value of $\mu$ are equal.

(b)

To determine

The explanation about why a large random sample gives more trustworthy results than a small random sample.

Explanation of Solution

Here, if a distribution is large then it can be used to make more precise estimates because a larger sample gives more information about the distribution.

Hence, it can be concluded that a large random sample gives more trustworthy results than a small random sample.