Lecture3_Part3 - From Sample to Population Sampling...

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SUNY at Albany - Department of Economics Eco 320 • Economic Statistics From Sample to Population Sampling Distribution
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1. The Big Idea of Statistics---Sampling Distribution A. Choosing a random sample from a population and calculating a statistic such as sample mean is a random phenomenon. B. The sampling distribution of a statistic tells us what values the statistic takes in repeated samples from the same population and how often it takes those values. C. We think of a sampling distribution as assigning probabilities to the values the statistic can take. Because there are usually many possible values, sampling distributions are often described by a density curve such as a Normal curve. SUNY at Albany - Department of Economics Eco 320 • Economic Statistics
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[Example] Opinion on a Constitutional Amendment--- Revisited A. Take a random sample of 2527 adults. Ask each whether they favor a constitutional amendment that would define marriage as being between a man and a woman. The proportion who say “Yes” B. is the sample proportion . Do this 10000 times and collect the 10000 sample proportions from the 10000 samples. The histogram shows the distribution of 10000 when the truth about the population is that 50% would favor such an amendment. C. The results of random sampling are random : we can’t predict the outcome of one sample, but the figure shows that the outcomes of many samples have a regular pattern. SUNY at Albany - Department of Economics Eco 320 • Economic Statistics 2527 yes" " say number who ˆ p p ˆ p ˆ p ˆ
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[Example] Opinion on a Constitutional Amendment--- Revisited (cont’d) SUNY at Albany - Department of Economics Eco 320 • Economic Statistics
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[Example] Opinion on a Constitutional Amendment--- Revisited (cont’d) A. The regular pattern of repeated random samples is one of the big ideas of statistics.
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