07DistofMeans

# 07DistofMeans - Statistical Techniques I EXST7005...

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Statistical Techniques I EXST7005 Distribution of Sample Means

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OBJECTIVES Usually we will be testing hypotheses about means. We will need some additional information about the nature of means of samples in order to do hypothesis tests.
Distribution of Sample Means Means are the basis for testing hypotheses about μ , the most common types of hypothesis tests. Imagine a POPULATION from which we are drawing samples. Population size = N Mean = μ Variance = σ 2 Parent population values are: Yi = Y1, Y2, Y3 , . .. , YN

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Distribution of Sample Means (continued) The samples of size n form a DERIVED POPULATION There are Nn possible samples of size n that can be drawn from a population of size N (sampling WITH replacement). for each sample we calculate a mean f8e5 Yk = Σ Yi/n where k = 1, 2, 3, . .. , Nn
Distribution of Sample Means (continued) The Derived Population of Means of samples o size n Population size = Nn Mean = μf8e5 Y Variance = σ2f8e5 Y Derived population values f8e5 Yk = f8e5 Y1, f8e5 Y2, f8e5 Y3, . .. , f8e5 YNn

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Distribution of Sample Means (continued) Mean of the DERIVED POPULATION μf8e5 Y = Σf8e5 Yk/Nn where k = 1, 2, 3, . .. , Nn Variance of the DERIVED POPULATION σ 2 f8e5 Y = Σ(f8e5 Yk- μ )2/Nn where k = 1, 2, 3, . .. , Nn n = the sample size N = the population size Population size = Nn
Example of a Derived Population Parent Population: Yi = 0, 1, 2, 3 μ = Σ Yi/N = 6/4=1.5 σ 2 = Σ( Yi- μ )2/N = [(0-1.5)2+(1-1.5)2+(2-1.5)2+(3 1.5)2]/4 = 5/4 = 1.25 σ = 1.12 Original Population 0.00 0.25 0 1 2 3 r.f.

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The Derived Population where n = 2 and
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07DistofMeans - Statistical Techniques I EXST7005...

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