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# Chapter 7 Distribution of Sample Means

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## Mary Stacy

on 5 March 2013

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#### Transcript of Chapter 7 Distribution of Sample Means

Natural Discrepancy
Amount of Error
Between a sample statistic and
corresponding population parameter Sampling Error Samples are variable
They are not all the same
Contains different individuals, things
Have different scores
Have different sample means Why??? Not a bad thing...it just happens A distribution of statistics obtained by
selecting all the possible samples of a
specific size from a population What is a Sampling
Distribution? Example 7.1 N = 4, EX = 20, Mean = 5 All possible samples
from 7.1 if n = 2 Forming the normal
shaped distribution Sample means should pile up around Population mean
"Pile" of sample means should form a normal shaped distribution
Larger the sample size, the closer the sample means should be to the population mean Logic of the
Sampling Distribution Central Limit Theorem For any population with a mean µ and standard deviation σ , the distribution of sample means for sample size will have a mean of µ and a standard deviation of σ/√n and will approach a normal distribution as n approaches infinity. Describes distribution for ANY Population
DSM apporaches a Normal Distribution Rapidly
n = 30; the distribution is almost perfectly normal Central Limit Theorem Shape - Central Tendency - Variability Shape
Central Tendency
Variability 3 Characteristics of DSM Remember what the Standard Deviation is telling us Standard Error of the M Purpose of SEM Describes the Distribution of the Sample Means
Measures how well an individual SAMPLE mean represents the entire distribution As a sample size (n) increases, the standard error decreases
When the sample consists of a single score (n = 1), the standard error is the same as the standard deviation to remember... Computation σ
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