Question

Identify each quantity as a parameter or a statistic

(a) $\mu$ (b)$s$ (c)$\overline{x}$ (d)$\sigma$

Short answer

(a) $\mu$is parameter quantity.

(b) $s$is statistic quantity.

(c) $\overline{x}$is statistic quantity.

(d) $\sigma$is parameter quantity.

Step-by-step solution

Part(a) Step 1: Given Information

We are given quantity$\mu$

We need to identify whether quantity is parameter or statistic

Part(a) Step 2: Explanation

A parameter is a number that describes the entire population characteristics .

A statistic is a number that describes characteristics of a sample.

Greek and capital letters typically refer to populations, but Latin and lower-case letters usually refer to samples.

From above definitions we can elaborate that

$\mu$is parameter quantity.

Part(b) Step 1: Given Information

We are given quantity $s$

We need to identify whether quantity is parameter or statistic

Part(b) Step 2: Explanation

A statistic is a number that describes characteristics of a sample.

Greek and capital letters typically refer to populations, but Latin and lower-case letters usually refer to samples.

From above definitions we can elaborate that

$s$ is a statistic quantity.

Part(c) Step 1: Given Information

We are given quantity $\overline{x}$

We need to identify whether quantity is parameter or statistic

Part(c) Step 2: Explanation

A statistic is a number that describes characteristics of a sample.

Greek and capital letters typically refer to populations, but Latin and lower-case letters usually refer to samples.

From above definitions we can elaborate that

$\overline{x}$is a statistic quantity.

Part(d) Step 1: Given Information

We are given quantity $\sigma$

We need to identify whether quantity is parameter or statistic

Part(d) Step 2: Explanation

A parameter is a number that describes the entire population characteristics .

A statistic is a number that describes characteristics of a sample.

Greek and capital letters typically refer to populations, but Latin and lower-case letters usually refer to samples.

From above definitions we can elaborate that

$\sigma$ is a parameter quantity.