School

York UniversityDepartment

Operations Management and Information SystemCourse Code

OMIS 2010Professor

Alan MarshallThis

**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

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