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Unformatted text preview: BPS  5th Ed. Chapter 11 1 Chapter 11 Sampling Distributions BPS  5th Ed. Chapter 11 2 Sampling Terminology ◆ Parameter – fixed, unknown number that describes the population ◆ Statistic – known value calculated from a sample – a statistic is often used to estimate a parameter ◆ Variability – different samples from the same population may yield different values of the sample statistic ◆ Sampling Distribution – tells what values a statistic takes and how often it takes those values in repeated sampling BPS  5th Ed. Chapter 11 3 Parameter vs. Statistic A properly chosen sample of 1600 people across the United States was asked if they regularly watch a certain television program, and 24% said yes . The parameter of interest here is the true proportion of all people in the U.S. who watch the program, while the statistic is the value 24% obtained from the sample of 1600 people. BPS  5th Ed. Chapter 11 4 Parameter vs. Statistic ◆ The mean of a population is denoted by µ – this is a parameter . ◆ The mean of a sample is denoted by – this is a statistic . is used to estimate µ . x x ◆ The true proportion of a population with a certain trait is denoted by p – this is a parameter . ◆ The proportion of a sample with a certain trait is denoted by (“ phat ”) – this is a statistic . is used to estimate p . p ˆ p ˆ BPS  5th Ed. Chapter 11 5 The Law of Large Numbers Consider sampling at random from a population with true mean µ . As the number of (independent) observations sampled increases, the mean of the sample gets closer and closer to the true mean of the population. ( gets closer to µ ) x BPS  5th Ed. Chapter 11 6 The Law of Large Numbers Gambling ◆ The “house” in a gambling operation is not gambling at all – the games are defined so that the gambler has a negative expected gain per play (the true mean gain after all possible plays is negative) – each play is independent of previous plays, so the law of large numbers guarantees that the average winnings of a large number of customers will be close the the (negative) true average BPS  5th Ed. Chapter 11 7 Sampling Distribution ◆ The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size ( n ) from the same population – to describe a distribution we need to specify...
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This note was uploaded on 08/27/2011 for the course MA 116 taught by Professor Muntheralraban during the Summer '11 term at Montgomery CC.
 Summer '11
 MuntherAlraban
 Statistics

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