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Unformatted text preview: Chapter 7: Sampling Distributions Section 7.1 How Likely Are the Possible Values of a Statistic? The Sampling Distribution Learning Objectives 1. Statistic vs. Parameter 2. Sampling Distributions 3. Mean and Standard Deviation of the Sampling Distribution of a Proportion 4. Standard Error 5. Sampling Distribution Example 6. Population, Data, and Sampling Distributions Learning Objective 1: Statistic and Parameter A statistic is a numerical summary of sample data such as a sample proportion or sample mean A parameter is a numerical summary of a population such as a population proportion or population mean. In practice, we seldom know the values of parameters. Parameters are estimated using sample data. We use statistics to estimate parameters. Learning Objective 2: Sampling Distributions Example: Prior to counting the votes, the proportion in favor of recalling Governor Gray Davis was an unknown parameter . An exit poll of 3160 voters reported that the sample proportion in favor of a recall was 0.54. If a different random sample of about 3000 voters were selected, a different sample proportion would occur. The sampling distribution of the sample proportion shows all possible values and the probabilities for those values. Learning Objective 2: Sampling Distributions The sampling distribution of a statistic is the probability distribution that specifies probabilities for the possible values the statistic can take. Sampling distributions describe the variability that occurs from study to study using statistics to estimate population parameters Sampling distributions help to predict how close a statistic falls to the parameter it estimates Learning Objective 3: Mean and SD of the Sampling Distribution of a Proportion For a random sample of size n from a population with proportion p of outcomes in a particular category, the sampling distribution of the proportion of the sample in that category has n p) p(1 deviation standard p Mean = = Learning Objective 4: The Standard Error To distinguish the standard deviation of a sampling distribution from the standard deviation of an ordinary probability distribution, we refer to it as a standard error. Learning Objective 5: Example: 2006 California Election If the population proportion supporting the reelection of Schwarzenegger was 0.50, would it have been unlikely to observe the exitpoll sample proportion of 0.565? Based on your answer, would you be willing to predict that Schwarzenegger would win the election? Learning Objective 5: Example: 2006 California Given that the exit poll had 2705 people and assuming 50% support the reelection of Schwarzenegger, Find the estimate of the population proportion and the standard error: 0096 ....
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This note was uploaded on 08/01/2011 for the course STAT 101 taught by Professor Thomas during the Spring '11 term at Pennsylvania State University, University Park.
 Spring '11
 Thomas
 Standard Deviation

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