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STATISTICAL INFERENCE

STATISTICAL INFERENCE. Statistical Inference uses sample data and statistical procedures to: Estimate population parameters; or Test whether or not a population parameter is likely to satisfy some specified value. STATISTICAL INFERENCE. Estimation of population parameters

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STATISTICAL INFERENCE

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  1. STATISTICAL INFERENCE Statistical Inference uses sample data and statistical procedures to: • Estimate population parameters; or • Test whether or not a population parameter is likely to satisfy some specified value.

  2. STATISTICAL INFERENCE • Estimation of population parameters • The process of using a statistic to infer about the value of an unknown parameter with a specified level of certainty • Test whether a population parameter is likely to satisfy some specified value • The use of sample data to accept or to reject a statement about a parameter value or about a population distribution

  3. Properties of Point Estimators • Bias describes the location of an estimator; • Efficiency is a measure of the amount of variation in the sampling distributions for alternative estimators of a parameter; • Consistency describes how the sampling distribution of an estimator concentrates around the parameter values as the sample size increases; and • Sufficiency is a measure of the use of information.

  4. ESTIMATION The process of using a statistic to infer about the value of an unknown parameter with a specified level of certainty: • Large Sample 100(1 - )% Confidence Interval for ; • Small Sample 100(1 - )% Confidence Interval for ; and • Confidence Limit for 

  5. Interval Estimation Procedure • Want to use X to estimate X. • How reliable is a point estimate? • Develop a measure of reliability by finding an interval of numbers within which we expect the true value of the population mean to be contained. • Have X, but do not know X.

  6. Interval Estimation Procedure • Large-Sample 100( 1 -  )% Confidence Interval for Xis X + Z/2  X. • The interval X + 1.96 X is called a Large-Sample 95% Confidence Interval for the population mean.

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