Explain, in Words That a Non-Statistics Student Would Understand, Why

question 23

Essay

Explain, in words that a non-statistics student would understand, why the standard deviation of the various sample means taken from a population is smaller than the standard deviation of the individuals in the population? (In the first situation, assume all samples are of the same size, and that size is large.)

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Definitions:

Degrees of Freedom

The sum of independent quantities or values able to be set for a statistical distribution.

Population Variances

A measure of the variance within an entire population, indicating the average of the squared differences from the mean.

Test Statistic

A standardized value calculated from sample data during a hypothesis test; used to decide whether to reject the null hypothesis.

Confidence Interval

A variety of values taken from statistics of a sample, presumed to hold the value of a not yet known population attribute.