econ cheat sheet4

econ cheat sheet4 - Sampling Distributions A sampling...

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Sampling Distributions… A sampling distribution is created by, as the name suggests, sampling. The method we will employ relies on the rules of probability and the laws of expected value and variance to derive the sampling distribution. For example, consider the roll of one and two dice… Sampling Distribution of the Mean… A fair die is thrown infinitely many times, with the random variable X = # of spots on any throw. The probability distribution of X is: …and the mean and variance are calculated as well: Sampling Distribution of Two Dice A sampling distribution is created by looking at all samples of size n=2 (i.e. two dice) and their means… While there are 36 possible samples of size 2, there are only 11 values for x(bar), and some (e.g. x(bar)=3.5) occur more frequently than others (e.g. x(bar)=1). Generalize. .. We can generalize the mean and variance of the sampling of two dice: …to n-dice: Centreal Limit Theorem…. The sampling distribution of the mean of a random sample drawn from any population is approxi- mately normal for a sufficiently large sample size. The larger the sample size, the more closely the sampling distribution of X(bar) will resemble a normal distribution. If the population is normal, then X is normally distributed for all values of n. If the population is non-normal, then X is approximately normal only for larger values of n. In most practical situations, a sample size of 30 may be sufficiently large to allow us to use the normal distribution as an approximation for the sampling distribution of X. Sampling Distribution of the Sample Mean 1. 2. 3. If X is normal, X(bar) is normal. If X is nonnormal, X(bar) is approximately normal for sufficiently large sample sizes. Note: the definition of “sufficiently large” depends on the extent of nonnormality of x (e.g. heavily skewed; multimodal) We can express the sampling distribution of the mean simple as: The summaries above assume that the population is infinitely large. However if the population is finite the standard error is where N is the population size and is the finite population correction factor .
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This note was uploaded on 11/11/2011 for the course ECON 100 taught by Professor Chandle during the Spring '11 term at UC Irvine.

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econ cheat sheet4 - Sampling Distributions A sampling...

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