1.4 Confidence Intervals and the Central Limit Theorem STAT 506 - Sampling Theory and Methods

1.4 Confidence Intervals and the Central Limit Theorem STAT 506 - Sampling Theory and Methods

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STAT 506 - Sampling Theory and Methods ANGEL Department of Statistics Eberly College of Science Home // Lesson 1: Introduction; Estimating Population Mean and Total under Simple Random Sampling 1.4 Confidence Intervals and the Central Limit Theorem Submitted by gfj100 on Mon, 11/30/2009 - 18:30 Unit Summary The confidence interval for μ, τ Finite population Central Limit Theorem Confidence Intervals The idea behind confidence intervals is that it is not enough just using sample mean to estimate the population mean. The sample mean by itself is a single point. This does not give people any idea as to how good your estimation is of the population mean. If we want to assess the accuracy of this estimate we will use confidence intervals which provide us with information as to how good our estimation is. A confidence interval, viewed before the sample is selected, is the interval which has a pre-specified probability of containing the parameter. To obtain this confidence interval you need to know the sampling distribution of the estimate. Once we know the distribution, we can talk about confidence. We want to be able to say something about θ, or rather because should be close to θ. So the type of statement that we want to make will look like this: Thus, we need to know the distribution of . In certain cases the distribution of can be stated easily. However, there are many different types of distributions.
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1.4 Confidence Intervals and the Central Limit Theorem STAT 506 - Sampling Theory and Methods

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