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Inferential Statistics

statistics that are used to interpret data and draw conclusions

Simple Random Sample

abbreviated SRS, this requires that every item in the population has an equal chance to be chosen and that every possible combination of items has an equal chance to exist. No grouping can be involved.

Systematic Sampling

A method of sampling in which you determine randomly where you want to start selecting in the sampling frame and then follow a rule to select every xth unit from the sampling frame list.

Sampling Fraction

The ratio of the size of the sample (n) to the size of the population (N).

Cluster sampling

dividing a population into subgroups (clusters) and forming a sample by randomly selecting clusters and including all individuals or objects in the selected clusters in the sample

Stratified Random Sampling

a process or selecting individuals from a population in such a way that the subgroups in the population are REPRESENTED in the sample, the population is divided into subpopulations and random samples are taken of each stratum.

Sampling distribution of the Mean

a distribution of sample statistics (all the possible sample means) for all samples of a given size randomly selected from the population.

Theoretical Sampling Distributions

The distribution of outcomes produced by an infinite number of randomly drawn samples or random subdivisions of a sample. This distribution identifies the proportion of times that each outcome of a study could be expected to occur as a result of chance. Provides info for describing: the shape, central tendency, and variability for distributions.

Central Limit Theorem

as the sample size (n) increases, the sampling distribution of the mean for simple random samples of n cases, taken from a population with a mean equal to µ and a finite variance equal to ⊕², approximates a normal distribution.

Sampling Distribution

a distribution of statistics obtained by selecting all the possible samples of a specific size from a population

I. As the sample size (n) increases, the variability of the sampling distribution of the mean decreases (standard error decreases).

II. Even when the population is not normally distributed, the shape of the sampling distribution of the mean becomes more like the normal as the sample size increases.

II. Even when the population is not normally distributed, the shape of the sampling distribution of the mean becomes more like the normal as the sample size increases.

2 Generalizations about Mean Sampling Distributions

Multistage Sampling

sampling schemes that combine several sampling methods at individual steps

Proportional Allocation

sampling in which the number of elements selected from a stratum is directly proportional to the size of the stratum relative to the size of the population

Unbiased Estimator

a sample statistic that is most likely to approximate the corresponding population parameter

Standard Error of the Mean

The standard deviation of the sampling distribution.

1. are normally Distributed

2. have a mean equal to μ

3. have a standard error equal to ⊕/√n

2. have a mean equal to μ

3. have a standard error equal to ⊕/√n

Sampling Distributions...

1. decreases in variability (standard error decreases)

2. becomes more like the normal distribution in shape

2. becomes more like the normal distribution in shape

As sampling size increases, the sampling distribution of the mean