Unit 8: Sampling Distribution

Differentiate between descriptive and inferential statistics

Concept of a sampling distribution

Central Limit Theorem and its importance

Mean and standard deviation for the
sampling distribution of the sample mean

Descriptive statistics
-Collecting, presenting, and describing data either for population or simple information.

Inferential statistics
-Drawing conclusions and/or making decisions concerning a population based only on sample data.

Defined as the process of selecting some observations (subjects) from all the observations (subjects) from a particular group or population.

Properties:

As the sample size gets large enough

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The sampling distribution becomes almost normal regardless of shape of population

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The mean of the sampling distribution will equal the mean of the population

Sampling distribution of X is approximately normal distributed if:

the population is normally distributed, or

sample size > or equal to 30 through CLT through the shape of population is not normal

Z-value for the sampling distribution of X

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x= sample mean
u= population mean
o= standard error of the mean

Sampling Distribution of Sample Mean

Why Sample?

High precision

Less costly

Less time consuming

Sampling theory is a study of the relationship that exist between a population and samples drawn from the population.

provide a logical basis for
using samples to make inferences about populations

Sampling theory

Used in determining whether observed differences between two samples are actually due to chance variation or whether they are significant