Supplement_5

# Supplement_5 - CONFIDENCE INTERVALS CONFIDENCE INTERVALS...

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≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ CONFIDENCE INTERVALS ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ CONFIDENCE INTERVALS Documents prepared for use in course C22.0103.001 , New York University, Stern School of Business The notion of statistical inference page 3 This section describes the tasks of statistical inference. Simple estimation is one form of inference, and confidence intervals are another. The derivation of the confidence interval page 5 This shows how we get the interval for the population mean, assuming a normal population with known standard deviation. This situation is not realistic, but it does a nice job of laying out the algebra. Discussion of confidence intervals and examples page 7 This gives some basic background and then uses illustrations of confidence intervals for a normal population mean and for a binomial proportion. Some examples page 13 Here are illustrations of intervals for a normal population mean and for a binomial proportion. Confidence intervals obtained through Minitab page 14 Minitab can prepare a confidence interval for any column of a worksheet (spreadsheet). Here’s how. However, Minitab has no special provision for computing confidence intervals directly from x and s or, in the binomial case, from ± p . revised by Avi Giloni Sept 2005 Gary Simon, 2003 Cover photo: Pansies. 1

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≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ CONFIDENCE INTERVALS ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ 2
))))) THE NOTION OF STATISTICAL INFERENCE ))))) A statistical inference is a quantifiable statement about either a population parameter or a future random variable. There are many varieties of statistical inference, but we will focus on just four of them: parameter estimation, confidence intervals, hypothesis tests, and predictions. Parameter estimation is conceptually the simplest. Estimation is done by giving a single number which represents a guess at an unknown population parameter. If X 1 , X 2 , …, X n is a sample of n values from a population with unknown mean µ , then we might consider using X as an estimate of µ . We would write µ = ± X . This is not the only estimate of µ , but it makes a lot of sense. A confidence interval is an interval which has a specified probability of containing an unknown population parameter. If X 1 , X 2 , …, X n is a sample of n values from a population which is assumed to be normal and which has an unknown mean µ , then a 1 - α confidence interval for µ is X ± /2; 1 n s n α− t . Here t α /2; n -1 is a point from the t table. Once the data leads to actual numbers, you’ll make a statement of the form “I’m 95% confident that the value of µ lies between 484.6 and 530.8.” A hypothesis test is a yes-no decision about an unknown population parameter. There is considerable formalism, intense notation, and jargon associated with hypothesis testing.

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Supplement_5 - CONFIDENCE INTERVALS CONFIDENCE INTERVALS...

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