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Chapter 9 Sampling Distribution Good Day!! Chapter 9 Sampling Distributions • Parameter – is a number that describes the population, like µ and σ • Statistic – is a number that can be computed from sample data without making use of any unknown parameters, like or s, x-bar. • Sampling Variability – how the value of a statistic varies in repeated random sampling. – Statisticians always ask: “What would happen if I took many samples of the same size from the same population?” Law of Large Numbers – Draw observations from any population with a finite mean, µ. As the number of observations drawn increases, the mean x-bar, of the observed values gets closer and closer to µ. • Unbiased Estimator – when a statistic is used to estimate a parameter, it is unbiased if the mean of its sampling distribution is equal to the true value of the parameter being estimated. Sampling Distribution – is the distribution of values taken by the statistic in all possible samples of the same size from the same population. -For example: the distribution of x-bar for each 100 samples taken from a particular population. -Even if the parent population is skewed or not normal, its sampling distribution will approach normal when n, the sample size is large. • Central Limit Theorem – Draw an SRS of size n from any population whatsoever, with mean µ, and standard deviation σ. When n is large, the sampling distribution of the sample mean x-bar, is close to a normal distribution, N(µ,σ/√n) • Homework p. 457 #s1-4 » p. 468 # 9 » p. 485 & 486 #s 26 & 28 » p. 491 & 492 #s 31 – 34 Lets do #30 together in class p.491