Question

Consider the quantities${\mu }_1,{\sigma }_1,{\overline{x}}_1,s_1,{\mu }_2,{\sigma }_2,{\hat{x}}_2$, and $s_2$.

a. Which quantities represent parameters and which represent statistics?

b. Which quantities are fixed numbers and which are variables?

Short answer

(a) ${\mu }_1,{\sigma }_1,{\mu }_2$, and ${\sigma }_2$are parameters and ${\overline{x}}_1,s_1,{\overline{x}}_2$, and $s_2$are statistics.

(b)${\mu }_1,{\sigma }_1,{\mu }_2$and ${\sigma }_2$are flxed numbers, while ${\overline{x}}_1,s_1,{\overline{x}}_2$, and $s_2$are variable numbers.

Step-by-step solution

Part (a) Step 1: Given information  

Given in the question that, from the quantities

${\mu }_1,{\sigma }_1,{\overline{x}}_1,s_1,{\mu }_2,{\sigma }_2,{\hat{x}}_2$, and $s_2$.we need to find that Which quantities represent parameters and which represent statistics.

Part (a) Step 2: Explanation

The following are the quantities:

${\mu }_1,{\sigma }_1,{\overline{x}}_1,s_1,{\mu }_2,{\sigma }_2,{\hat{x}}_2$and $s_2$

According to the definition, parameters are numerical values that define data for an entire population, whereas statistics are numerical quantities that characterise data from a sample, i.e. a subset of the entire population.

Quantities are given:${\mu }_1,{\sigma }_1,{\overline{x}}_1,s_1,{\mu }_2,{\sigma }_2,{\hat{x}}_2$and $s_2$

Here ${\mu }_1,{\sigma }_1,{\mu }_2$, and ${\sigma }_2$are parameters and ${\overline{x}}_1,s_1,{\overline{x}}_2$, and $s_2$are statistics.

Part (b) Step 1: Given information  

Given in the question that, from the quantities

${\mu }_1,{\sigma }_1,{\overline{x}}_1,s_1,{\mu }_2,{\sigma }_2,{\hat{x}}_2$and $s_2$we need to find that which quantities are fixed numbers and which are variables.

Part (b) Step 2: Explanation

The following are the quantities:

${\mu }_1,{\sigma }_1,{\overline{x}}_1,s_1,{\mu }_2,{\sigma }_2,{\hat{x}}_2$and $s_2$

As described by the definition, statistics are numerical numbers that characterise data from a sample, i.e. a subset of the complete population. Statistics are numerical quantities that characterise data from a sample, i.e. a subset of the entire population, as defined by the definition. Parameters are numerical values that summarise data for a complete population, whereas statistics are numerical quantities that characterise data from a sample, i.e. a subset of the entire population, as defined by the definition.

Quantities are given , ${\mu }_1,{\sigma }_1,{\overline{x}}_1,s_1,{\mu }_2,{\sigma }_2,{\overline{x}}_2$and $s_2$

Here ${\mu }_1,{\sigma }_1,{\mu }_2$, and ${\sigma }_2$are parameters and ${\overline{x}}_1,s_1,{\overline{x}}_2$, and $s_2$are statistics.

Because the sample size utilised might affect the numerical value of statistics,. As a result ${\mu }_1,{\sigma }_1,{\mu }_2$and ${\sigma }_2$are fixed numbers, while ${\overline{x}}_1,s_1,{\overline{x}}_2$, and $s_2$are variable numbers.