Question

In words, define the random variables $X$ and$\overline{X}$.

Short answer

The sample mean, $\overline{x}$ is the point estimate for the population mean $\mu$.

Step-by-step solution

Given Information 

The random variables are$X$and$\overline{X}$.

Explanation 

The sample mean, $\overline{x}$is the point estimate for the population mean $\mu$.

Suppose that $X_1,X_2,\dots ,X_n$, is a random sample from a normal distribution with unknown mean $\mu$, than test statistic

$\overline{X}=\frac{X_1+X_2+\cdots +X_n}{n},$

is normally distributed with mean $\mu$and variance localid="1648836325806" ${\sigma }^2/n$.

Explanation

It is often necessary to construct confidence intervals on a population proportion. For example, suppose that a random sample of size $n$ has been taken from a large (possibly infinite) population and that $X(\le n)$ observations in this sample belong to a class of interest. Then

$\overline{P}=\frac{X}{n}$

is a point estimator of the proportion of the population $p$ that belongs to this class.