15ConfidenceIntervals

15ConfidenceIntervals - Statistical Techniques I EXST7005...

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Unformatted text preview: Statistical Techniques I EXST7005 Confidence Intervals Confidence intervals An expression of what we believe to be a range of values that is likely to contain the true value o some parameter is called a confidence interval. We can calculate confidence intervals for mean ( ) and variances ( ). t and Z tests confidence intervals start with a t o Z probability statement. P t t t a a ( )- =- 2 2 1 P t Y S t a Y a ( )- - =- 2 2 1 Confidence intervals for t and Z distributions Confidence intervals for t and Z distributions (continued) Which is modified to express an interval about instead of t (or Z). P t S Y t S a Y a Y ( )- - =- 2 2 1 P Y t S Y t S a Y a Y ( )- + -- =- 2 2 1 Confidence intervals for t and Z distributions (continued) The final form is given below. The expression for Z has an identical derivation. P Y t S Y t S a Y a Y ( )- + =- 2 2 1 P Y Z Y Z a a Y Y ( )- + =- 2 2 2 2 1 Confidence intervals for t and Z distributions (continued) A common short notation for the interval in the probability statement is given as Y t S a Y 2 Confidence intervals for variance Variances follow a Chi square distribution. The confidence interval for variance is based on the Chi Square distribution....
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This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.

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15ConfidenceIntervals - Statistical Techniques I EXST7005...

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