AF Chaper 7 handouts FA08

AF Chaper 7 handouts FA08 - The Process of a Statistical...

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1 STAT 2000 Chapter 7 Confidence Intervals Agresti-Franklin Identify Objective Question(s) about a population Design Study and Collect Data Select a sample from a population Make Inferences The Process of a Statistical Study Describe Data Organize and present sample data about a population Make predictions and draw conclusions Principles of Probability As we begin to talk about Inference, let’s look back at what we have done before, and why. Gathering Data – Statistical inference methods assume that data was collected with some type of randomization. Sampling Distributions – Probability calculations Sampling Distributions Probability calculations used in inference refer to sampling distributions. Two types of Inference Estimation – Chapter 7 Hypothesis Testing – Chapters 8-9 A point estimate of a population parameter is an estimate given by a single value. Sample Statistics are point estimates of Population Parameters. Sample Population Statistic Parameter Mean μ Standard Deviation s σ Proportion p x ˆ p An interval estimate of a population parameter is given by two values between which we expect to have the population parameter. (Why would we want an interval estimate instead of a point estimate?) Our interval estimate is given by point estimate ± margin of error The margin of error is how much we expect to be *off*. SAMPLE: Interviews with 706 likely voters, conducted by telephone on July 9-11, 2004. MARGIN OF ERROR: ± 4% The point estimate of the proportion that would vote for Bush was 0.46. The interval estimate would be 0.46 ± 0.04, and we would write this as (0.42, 0.50). The lower limit is 0.42, and the upper limit is 0.50.
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2 The interval estimate that we will construct is called a confidence interval . Our confidence is in the method that we use to construct this interval. The level of confidence most often used is .95. We say we have 95% confidence that the interval we construct contains the parameter. What we mean is that our method will give correct results (interval will contain the true population value) 95% of the time. In reality, we only take one sample and calculate just one confidence interval. The diagram to the right shows what would happen if we took many samples. For each sample, a sample proportion is calculated and is represented by the center dot. An interval is constructed. The line down the center is the true population proportion. The interval constructed does not always contain the true population value. When we construct a 95% confidence interval, we do not know whether or not the interval we construct contains the true population value. We know that ~ 95% of the intervals we could construct using this same method will contain the population value, and ~ 5% will not. We say we are 95% confident that our interval contains the true population proportion.
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AF Chaper 7 handouts FA08 - The Process of a Statistical...

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