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Unformatted text preview: 5.5 Sampling Distributions In this section, we discuss the following: • The Sampling Distribution of a Statistic • The Properties of Sampling Distributions Example 1. Experiment: Suppose a digit from 0 to 9 is chosen at random. Random variable X: Outcome of the experiment: Their possible values are 0, 1, … , 9. Probability distribution of X is: P( x )=1/10 , for every value x . Sampling distribution : Suppose, many samples of different sizes are selected. For each sample, the mean (which itself may be considered as a random variable) is calculatrd. The probability distribution of sample means is called sampling distribution of sample mean. 1 Goal: The sampling distribution for a statistic allows us to use the statistic to estimate the value of a population parameter with a certain known degree of certainty. Some examples are: Population Parameter Sample Estimator Proportion π p Mean μ x Variance σ 2 s 2 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 (unbisedness, will be discussed later) 2 The spread tends to be smaller for larger samples (The sample variance of statistics decreases with n ) 3 For large samples, sampling distributions become more like normal distribution. ( This is called the CLT ) 2 Definition . A statistic T is unbiased for θ if θ = ) ( T E for all θ ....
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 Summer '08
 Palaniappan
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