This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ....
View
Full Document
 Summer '08
 Palaniappan
 Standard Deviation, Variance, 2%, $3.00, $0.15

Click to edit the document details