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.
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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
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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
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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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