FIT Confidence Interval Concepts

FIT Confidence Interval Concepts - FIT Statistics Handout...

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FIT Statistics Handout Confidence Interval Estimation Procedures and Exercises Dr. Kenneth W. Lewis ALU/CPCE/DAS/OR 1 Sometimes, you may want to know the answer to an ethereal or gossamer question such as, how many grains of sands are there on the typical beach, how many stars can you see on a clear night, how tall on average are redwood trees of the pacific northwest, or what is the average number of days it takes to process a certain personnel action? Since we don’t know the answer to that last question, the previous questions, nor will we ever know it, we will need to determine some way to estimate that answer. We may use point estimates, one value estimates to guess what the true answer is, or we may use something called interval estimates to arrive at what the possible true answer may be. Either way, we need to first discuss what an estimator is, what its properties are and how we arrive at using certain estimators. So let’s begin. When we want to describe some quantitative characteristic of an entire population, we typically take a sample from that population, compute an estimate of that characteristic and then use it to make an inference or to derive at some conclusion based on observable behavior. To the extreme, “It has rained for the last four Tuesdays; therefore I infer or generalize that it will rain every Tuesday.” I have made an inference about rain on Tuesdays, based on a sample of collected and analyzed data. Sometimes my inferences are correct and sometimes they are not correct. It would probably not make sense to collect data on rain on Wednesdays to make an inference about rain on Tuesdays. It is not practical to take sample data about how often it rains in the tropical rain forests of South America to make an inference about rain in southern Arizona. To the not so extreme, you don’t need to drink a whole quart of milk to determine if it is sour or spoiled. A small sample is usually sufficient to help you make an intelligent and accurate inference about the condition of that container of milk. We compute a sample statistic from sample data to estimate a population parameter. How do we sample? There are typically four methods of sampling behavior from a population of observable behaviors. They include: Simple Random Sampling: Each element is selected from one population and is also selected independently and with the same probability of getting picked as any other element. Systematic Random Sampling: Start at some random point in the list of elements in that population of interest and pick every nth element until you have selected the desired number of observations for your sample.
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FIT Statistics Handout Confidence Interval Estimation Procedures and Exercises Dr. Kenneth W. Lewis ALU/CPCE/DAS/OR 2 Stratified Random Sampling:
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