201 Lectures 2 - Unit 2 Stat 201 Ramón V León 1 Statistics 201 Introduction to Statistics Ramón V León Unit 2 Inference for Single Samples Unit

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Unformatted text preview: 3/30/2008 Unit 2 - Stat 201 - Ramón V. León 1 Statistics 201: Introduction to Statistics Ramón V. León Unit 2: Inference for Single Samples 3/30/2008 Unit 2 - Stat 201 - Ramón V. León 2 Applications: • Monitor the mean of a manufacturing process to determine if the process is under control • Evaluate the precision of a laboratory instrument measured by the variance of its readings • Prediction intervals which is a method for estimating future observations from a population. By using the central limit theorem (CLT), inference procedures for the mean of a normal population can be extended to the mean of a non-normal population when a large sample is available Inference About the Mean and Variance of a Normal Population 3/30/2008 Unit 2 - Stat 201 - Ramón V. León 3 Inferences on Mean (Large Samples) ( ) 2 2 Inferences on will be based on the sample mean , which is an unbiased estimator of with variance . For large sample size , the CLT tells us that is approximately , distributed, even if X n n X N n μ σ μ μ σ • • 2 2 the population is not normal. Also for large , the sample variance may be taken as an accurate estimator of with neglible sampling error. If 30, we may assume that in the formulas. n s n s σ σ • ≥ = 3/30/2008 Unit 2 - Stat 201 - Ramón V. León 4 Sample Size Determination for a z-interval [ ] Suppose that we require a (1- )-level two-sided CI for of the form , with a margin of error x E x E E α μ − + i 2 2 2 Set and solve for , obtaining z E z n n E n α α σ σ ⎡ ⎤ = = ⎢...
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This note was uploaded on 04/07/2008 for the course STAT 201 taught by Professor Leon during the Spring '08 term at University of Tennessee.

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201 Lectures 2 - Unit 2 Stat 201 Ramón V León 1 Statistics 201 Introduction to Statistics Ramón V León Unit 2 Inference for Single Samples Unit

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