# Review04 - CONFIDENCE INTERVALS Some people are still...

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CONFIDENCE INTERVALS Some people are still confused with confidence intervals. First, is the understanding of what a confidence interval is. As you remember from STA2023 a confidence interval is the interval computed from the data that is supposed to capture the actual population parameter with a certain level of confidence. For example the confidence interval computed based on the sample mean ¯ X is supposed to capture the population mean μ , the confidence interval computed based on the ˆ p is supposed to capture the population p . The confidence level indicates the likeness of the invent to happen. For example 95% confi- dence interval stands for the following: If we get 100 different samples and get 100 different estimates that correspond to those samples and produce 100 intervals using those estimates at least 95 out of the 100 intervals that we produce will capture actual parameter. (This was the exam question to interpret the confidence interval.) All confidence intervals look the same: ESTIMATE ¨ ME Where ESTIMATE is the estimate of the parameter that we compute from the data (like the sample mean ¯ X is the estimate of population mean μ , the sample proportion ˆ p is the estimate of the population proportion p , ¯ X 1 ¡ ¯ X 2 is the estimate of the difference between population means of two groups μ 1 ¡ μ 2 ). Parameters of interest are constants and they do not depend on the data in our sample. On the contrary estimates are random and every sample will give you different estimate. For example if I take 100 samples I will get 100 different sample means but we have only one population mean and it is always the same regardless how many samples I will take. We usually put a “hat” to emphasize that we have the estimate of the parameter. It will be reasonable to use

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## This note was uploaded on 01/08/2012 for the course STA 3024 taught by Professor Ta during the Summer '08 term at University of Florida.

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Review04 - CONFIDENCE INTERVALS Some people are still...

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