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Unformatted text preview: C22.0103: Statistics for Business Control: Regression and Forecasting Hong Luo Section 003, Spring 2009 Tue/Thu/Fri, 11:00  12:15pm, Tisch 200 Stern School of Business New York University Inference Introduction to Inference Confidence Interval Hypothesis Testing pValue Application in Regressions Inference Based on Two Samples Introduction to Inference Confidence Interval Hypothesis Testing pValue Application in Regressions Inference Based on Two Samples Inference I The goals of inference include I to estimate the value of an unknown population parameter I point estimate I interval estimate (confidence interval) I to make decisions about how the value of a parameter relates to a specific numerical value. i.e., is it less than, equal to, or greater than the specified number? I hypothesis testing I pvalue I “Statistics is never having to say you’re certain”. (Tee shirt, American Statistical Association) I It is not enough to provide a guess (point estimate) for the parameter. We also have to say something about how far such an estimator is likely to be from the true parameter value. Identifying Target Parameters The unknown population parameter that we are interested in estimating is called the target parameter . I μ : population mean (quantitative) I e.g. the mean gas mileage for a new car model I e.g. the mean amount of money owed by delinquent debtors I p : population proportion (qualitative data with two outcomes) I e.g. the percentage of people who are in favor of Obama’s stimulus plan I e.g. the proportion of households that watch “American Idols” Introduction to Inference Confidence Interval Hypothesis Testing pValue Application in Regressions Inference Based on Two Samples Confidence Interval I Large sample confidence interval for a population mean I Small sample confidence interval for a population mean I Large sample confidence interval for a population proportion Point Estimator I A point estimator of a population parameter is a rule or formula that tells us how to use the sample data to calculate a single number that can be used as an estimate of the population parameter. I an overriding rule in statistics: the characteristics of a random sample will mimic (resemble) those of the population. e.g. I ¯ x = P n i =1 x i n is an estimator of μ I s = q P n i =1 ( x i ¯ x ) 2 n 1 is an estimator of σ I difference between an estimator and an estimate I an estimator is a random variable whose value depends on a sample not yet taken (e.g. ¯ x ) I an estimate is the value actually taken by the estimator for a given sample (e.g. ¯ x = 1 . 985) Large Sample Confidence Interval for Population Mean with Known Variance I Assume that σ 2 is known for the moment I This is an unrealistic assumption, but it allows us to give a simplified presentation which reveals many of the important issues I According to the central limit theorem, ¯ x ∼ N ( μ, σ 2 n ) I Let’s calculate the following interval (¯ x 1 . 96 σ ¯ x , ¯ x...
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 Spring '08
 KITSIKOPOULOS
 Normal Distribution, Null hypothesis, Statistical hypothesis testing

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