Chapter 11 part 1

Chapter 11 part 1 - STAT 2053 Elementary Statistics Chapter...

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Click to edit Master subtitle style 9/23/11 STAT 2053 – Elementary Statistics Chapter 11 – Sampling Distribtions

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9/23/11 Chapter 11 This chapter focuses on how we use data collected from a sample to find out information about the whole population. The nature of randomness will make our results wrong every so often. We will use probability to evaluate how often our results are right. 22 Obj10 Chapter 11
9/23/11 Chapter 11 33 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

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9/23/11 Parameters/Statistics Definition : A parameter is a number that describes a particular population. Example : For the Normal distribution, the parameters are μ and σ. In practice, we rarely know the true value of a parameter. 44 Obj101 Chapter 11
9/23/11 Parameters/Statistics Definition : A statistic is a number that can be calculated using only the data from a sample. The calculation does not use any unknown parameters. Some common statistics: n, , We often use a statistic to estimate an unknown parameter. 55 Obj102 x s 2 Chapter 11

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9/23/11 Chapter 11 66 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.
9/23/11 Chapter 11 77 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 (“ p-hat ”) – this is a statistic . is used to estimate p . p ˆ p ˆ

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9/23/11 Sample Means Recall that, in Chapter 3, we defined μ as the mean of our density curve, or the shape of our histogram if we included everybody. Since our population consists of everybody, we can also say that μ is the population mean . In general, we do not know the true value of μ for our population. We can estimate it using the sample mean, . 88 Obj109 x Chapter 11
Sample Means Example : Suppose I roll a six sided die 5 times. Here are my results: 2 5 5 2 6 = The population mean, μ, is equal to 3.5. So even though our sample mean isn’t exactly equal to μ , it’s a decent estimate. 99

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This note was uploaded on 09/23/2011 for the course STAT 2053 taught by Professor Staff during the Fall '08 term at Oklahoma State.

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Chapter 11 part 1 - STAT 2053 Elementary Statistics Chapter...

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