chapter 3 - Chapter 3 What Do Statistics Tell Us?...

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Chapter 3 What Do Statistics Tell Us?
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Motivation According to a Gallop Poll conducted from July 2003 to February 2004, between 49 and 53 percent of Americans support an amendment to ban same sex marriages. N = 209 million Americans n = 2527 What does this statement mean?
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Outline From Sample to Population Sampling Variability Margin of Error Confidence Statements Sampling from a large population
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From Sample to Population
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Definitions Recall Population – entire group of individuals we want information about Ex. All 209 million Americans Sample – part of the population data is collected upon 2527 American Point of a sample is to learn about population
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Definitions A population parameter is a number that describes a population. Don’t usually know the exact value Ex. proportion of 209 million Americans against same sex marriage Denote p for proportion A sample statistic is a number that describes a sample. Can calculate the exact value using the data. Ex proportion of 2527 sampled Americans against same sex marriage is (1289/2527) Denote p ˆ
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Sampling Variability
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Motivation We know that __% of all MWF 9:05 STAT 110 students are sophomores, juniors, or seniors. If we take a SRS of students, will we get ___% of the sample are either sophomores, juniors, or seniors? If we take a biased sample of 5 students what will happen? Suppose that Gallop took a second SRS of 2527 Americans. Recall What are likely values of the sample proportion of Americans against same sex mairrage? 51 . ˆ = p
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Good Sampling Method Characteristics Small variability Sample proportion is “close” to population proportion In general: sample statistic is “close” to the population parameter Unbiased sample Definition: A sample is biased if the sample statistic tends to be larger than the population parameter or smaller Thus a sample is not biased if the sample statistic it just as likely larger than the population parameter as it is likely to be smaller
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Which sampling method is more variable? n =100
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chapter 3 - Chapter 3 What Do Statistics Tell Us?...

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