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

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

This preview shows half of the first page. to view the full 3 pages of the document. 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