Sample Survey Methods
Sample Survey Methods STAT 422
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This 2 page Class Notes was uploaded by Mr. Alex Berge on Friday October 23, 2015. The Class Notes belongs to STAT 422 at University of Idaho taught by Christopher Williams in Fall. Since its upload, it has received 29 views. For similar materials see /class/227939/stat-422-university-of-idaho in Statistics at University of Idaho.
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Date Created: 10/23/15
Review of probability distributions sample statistics in nite population Example Hypothetical data on number of television sets owned per household Number 0 1 2 3 4 Probability 2 4 2 1 1 Here the number of sets owned is the random variable and the set of probabilities above are its probability distribution Some important characteristics of a probability distribution are its expected value mean value variance and standard deviation Expected value ofy u Ey 2 y py 0 p0 1 p1 2 p2 3 p3 4 p4 0 2 1 4223 141 15 Variance ofy 62 Vy 2 y Ey 2py0 15221 15242 1522 3 152 1 4 152 1 145 The standard deviation of y is the square root of the variance here SDy sqrt145 120 In statistical studies we collect data from which we make inferences about unknown population parameters such as the population mean and variance For example we use sample statistics such as the mean variance and standard deviation to estimate the corresponding population parameters Example A sample of four households have the following numbers of TVs 2 0 1 3 The sample statistic values are For random samples from in nite populations the expected value of the sample mean is the true population mean and the variance of the sample mean equals the population variance divided by the sample size Also an unbiased estimate of the variance of the sample mean is the sample variance divided by the sample size Probability Sampling nite population Suppose we visit a small town with four houses denoted houses I II III and IV and the number of TVs in the houses are 1 3 4 and 4 respectively This is a simple example of a nite population the four houses with a single measurement the number of TV s Suppose we consider all possible samples of size n2 from this population of size N4 I II I III I IV II III II IV and III IV In probability sampling we assign a probability of drawing each possible sample If we assign a probability of 16 of drawing each of the six samples above then this is an example of a simple random sample without replacement Many other types of sampling designs exist and occasionally people draw samples with replacement to mimic the process of sampling from an in nite population
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