A Population Consists of These Values $3,5,8,14,17$ Find the Mean $\mu$

question 1

Essay

A population consists of these values: $3,5,8,14,17$ . Find the mean, $\mu$ , and standard deviation, $\sigma$ , of the population. List all samples of size $\mathrm { n } = 2$ that are obtained without replacement. Find the population of all values of $\bar { x }$ by finding the mean of each sample that you listed. Find the mean $\mu _ { x } ^ { - }$ and standard deviation $\sigma _ { x } ^ { - }$ for the population of sample means by using the formulas:
$$\mu _ { x } ^ { - } = \mu \text { and } \sigma _ { x } ^ { - } = \frac { \sigma } { \sqrt { n } } \sqrt { \frac { N - n } { N - 1 } }$$

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Definitions:

Experimental Research

A scientific method that seeks to determine cause-and-effect relationships by manipulating one variable while keeping others constant to observe the effects on the manipulated variable.

Cause-And-Effect

The principle that everything happens due to specific reasons, and that an action (cause) results in a certain outcome (effect).

Control Group

The control group in an experiment is the group that does not receive the experimental treatment, serving as a baseline to compare the effects of the treatment.

Room Temperature

Room temperature typically refers to a comfortable ambient temperature for humans, generally considered to be around 20°C to 22°C (68°F to 72°F).