# 5.4 - 5.4 Sampling Distributions Here we discuss the...

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5.4 Sampling Distributions Here we discuss the following: The Sampling Distribution The Properties of Sampling Distributions Point Estimators Parameter Estimator Proportion p p ˆ Mean μ x Variance σ 2 s 2 Example 1. Suppose a digit from 0 to 9 is randomly selected with replacement. Random variable X: Outcome of the experiment: The possible values are 0, 1, … , 9. Probability distribution of X is: P( x )=1/10 , for every value x . 1

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Sampling distribution : Suppose, many different samples size n=4 were selected. In each sample the mean was calculated (which itself is random variable). The probability distribution of sample means is sampling distribution of sample means. Goal: The sampling distribution for a statistic allows us to use the statistic to estimate the value of a population parameter with a known degree of certainty. 3

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General properties of sampling distributions 1 The sampling distribution of a statistic tends to center at the value of the population parameter estimated by the statistic (unbiasedness) 2 The spread tends to be smaller for larger samples (The sample variance
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5.4 - 5.4 Sampling Distributions Here we discuss the...

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