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Chapter

OMIS 2010 Chapter Notes -Sampling Distribution, Standard Error, Central Limit Theorem


Department
Operations Management and Information System
Course Code
OMIS 2010
Professor
Alan Marshall

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Sampling Distributions
Sampling Distributions of the Mean
-Is created by sampling draw sample of same size from a population or use rules of probability and
laws of expected value and variance to derive sampling distribution
-Sampling distribution of rolling a die can be created by drawing samples of size 2; tossing two dice
oMean of sampling distribution of x bar is same as mean of population of toss of a die
oVariance of sampling distribution of x bar is half of variance of population of the toss of a die
-Variance of sampling distribution of sample mean is variance of population divided by sample size
-Standard error of the mean: standard deviation of sampling distribution, for infinitely large populations
-As # of throws of the die increases, probability that sample mean will be close to population mean
increases
oSampling distribution of x bar becomes narrower as “n” increases; sampling distribution becomes
increasingly bell-shaped
-Central limit theorem: sampling distribution of mean of random sample drawn from any population is about
normal for sufficiently large sample size
oLarger the sample size, more closely the sampling distribution of x bar will resemble a normal
distribution
-Note: if population id normal then x bar is normally distributed for all values of n
-if population is non-normal then x bar is normal for ONLY LARGER VALUES OF N
-If population extremely non-normal (bimodal/highly skewed distribution) sampling distribution will also
be non-normal even for large values of “n”
Sampling Distribution of Mean of Any Population
-If population is finite, the standard error need to use different approach
-If population size is large relative to sample size, then finite population correction factor is close to 1 and
can be ignored
oPopulations that are at least 20 times larger than simple size are considered large
Creating Sampling Distribution Empirically
-Create distribution empirically y: actually tossing two fair dice repeatedly, calculate sample mean for
each sample, count # of times each value of “x bar” occurs and compute relative frequencies to
estimate theoretical probabilities
Using Sampling Distribution for Inference
-Za is the value of z such that area to right of Za under the standard normal curve is equal to A
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