IE 220PROBABILITY AND STATISTICS2009-2010 SpringChapter 7Sampling Distributions
Introduction•Parameters are numerical descriptive measures for populations.–For the normal distribution, the location and shape are described by and –For a binomial distribution consisting of ntrials, the location and shape are determined by p. •Often the values of parameters that specify the exact form of a distribution are unknown. •You must rely on the sample to learn about these parameters.
Sampling Distributions•Numerical descriptive measures calculated from the sample are called statisticsstatistics.•Statistics vary from sample to sample and hence are random variables.•The probability distributions for statistics are called sampling distributionssampling distributions.•In repeated sampling, they tell us what values of the statistics can occur and how often each value occurs.
Possible samples3, 5, 23, 5, 13, 2, 15, 2, 1Possible samples3, 5, 23, 5, 13, 2, 15, 2, 1xSampling DistributionsDefinition: The sampling distribution of a sampling distribution of a statisticstatisticis the probability distribution for the possible values of the statistic that results when random samples of size nare repeatedly drawn from the population.Population:3, 5, 2, 1Draw samples of size n= 3 without replacementPopulation:3, 5, 2, 1Draw samples of size n= 3 without replacement67.23/823/633/933.33/10Each value of x-bar is equally likely, with probability 1/4xp(x)1/42 3
Sampling DistributionsSampling distributions for statistics can be Approximated with simulation techniquesDerived using mathematical theorems