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Unformatted text preview: 1 CHAPTER 9: SAMPLING DISTRIBUTIONS Stats & Prob. for Bus. Mgmt (Stat1100) Jochem Chap 9: Sampling Distributions b Overview b Part 1: The Central Limit Theorem & the Sampling Distribution of a Mean b Part 2: The Sampling Distribution of a Proportion 2 b Part 3: The Sampling Distribution of the Difference between Two Means b Part 4: From here to Inference Part 1: The Central Limit Theorem & 3 Chap 9: Sampling Distributions the Sampling Distribution of a Mean b 1. Recall: b 1. Parameter s Is a number describing the population of the study and which is typically unknown . 4 Chap 9: Sampling Distributions s Examples: mean ( μ ), std dev ( σ ), variance ( σ 2 ) b 2. Statistic s a number describing the units in a sample that we (hopefully randomly) drew from the population s Examples: mean (xbar), std dev (s), variance (s 2 ) b 1. Recall: b 1. Parameter s Is a number describing the population of the study and which is typically unknown . 5 Chap 9: Sampling Distributions s Examples: mean ( μ ), std dev ( σ ), variance ( σ 2 ) b 2. Statistic s a number describing the units in a sample that we (hopefully randomly) drew from the population s Examples: mean (xbar), std dev (s), variance (s 2 ) b A statistic is used to estimate an unknown parameter. How? B Law of Large Numbers/Central Limit Theorem b 1. The Law of Large Numbers: b “Randomly draw n observations from any population with any distribution with finite mean μ . As n increases, the mean of the sample (xbar) gets closer and closer 6 Chap 9: Sampling Distributions to the true population mean μ .” s Example: “Avg. hours of TV watching per week in U.S.” ( Assume it was μ =25 and σ =7.) s Then: One sample, increasing sample size: By LLN: xbar B 25 s Why? Outliers are moderated by the mass of points close to true mean. b 1. Sampling Distribution b What if: many samples, each with a small sample size? b Procedure: s For i=1 to 1,000 7 Chap 9: Sampling Distributions begin s take a random sample of size N=10 s compute xbar, write it down. end s make a histogram of all collected xbars s this is “ the sampling distribution of the mean ” (aka Xbar) s Note that as all distributions, it has a shape, center and spread! Note the Capital letter X (it’s now a random variable) b 1. The Sampling Distribution of xbar 8 Chap 9: Sampling Distributions Source: Moore, p297 This is the sampling distribution (X bar) of the sample means (xbars). b 1. The Sampling Distribution b The population distribution of a variable is the histogram you’d get if you knew the variable for the full population. s = describes the individuals of the population Chap 9: Sampling Distributions 9 b The sample distribution of a variable is the histogram of one variable in your sample....
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This note was uploaded on 03/26/2012 for the course STAT 1100 taught by Professor Chiappetta during the Spring '08 term at Pittsburgh.
 Spring '08
 Chiappetta
 Central Limit Theorem

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