When Sampling Without Replacement from a Finite Population of Size $$\sigma _ { x } ^ { - } = \frac { \sigma } { \sqrt { n } } \sqrt { \frac { N - n } { N - 1 } }$$

question 139

Essay

When sampling without replacement from a finite population of size N, the following formula is used to find the standard deviation of the population of sample means: $$\sigma _ { x } ^ { - } = \frac { \sigma } { \sqrt { n } } \sqrt { \frac { N - n } { N - 1 } }$$ However, when the sample size n, is smaller than 5% of the population size, N, the finite population correction factor, $\sqrt { \frac { N - n } { N - 1 } }$ , can be omitted. Explain in your own words why this is reasonable. For $\mathrm { N } = 200$ nd the values of the finite population correction factor when the sample size is 10%, 5%, 3%, 1% of the population, respectively. What do you notice?

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Definitions:

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Independent Variable

A factor manipulated by the experimenter to investigate its effects on the dependent variable in a study.

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A design in which all levels of each independent variable are combined with all levels of the other independent variables. A factorial design allows investigation of the separate main effects and interactions of two or more independent variables.