part9 - Public Health 6450 Fall 2011 Andrew Mugglin and...

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Unformatted text preview: Public Health 6450 Fall 2011 Andrew Mugglin and Lynn Eberly Division of Biostatistics School of Public Health University of Minnesota ph6450@biostat.umn.edu Part 09 Review Revisiting Important Concepts Hypothesis Testing Where are we going? Previously: Interval estimates for when is known (use z * and ) Interval estimates for when is unknown (use t * and s ) Current topics: Revisiting important concepts Introduction to hypothesis testing: Ch.6.2 Hypothesis tests for when is known: Ch.6.2 (use z and ) Hypothesis tests for when is unknown: Ch.7.1 (use t and s ) (Interval estimates and hypothesis testing for the Binomial will be covered in Ch. 8.) Mugglin and Eberly PubH 6450 Fall 2011 Part 09 2 / 53 Review Revisiting Important Concepts Hypothesis Testing Standardizing to a normal distribution We compute probabilities that X (or X ) takes a range of values by first standardizing to a standard normal Z . The probability that X < a is Pr ( X < a ) = Pr X- < a- = Pr Z < a- . When we have an i . i . d . sample of X s, then Pr ( X < a ) = Pr X- / n < a- / n = Pr Z < a- / n . Mugglin and Eberly PubH 6450 Fall 2011 Part 09 3 / 53 Review Revisiting Important Concepts Hypothesis Testing Computing CIs for the mean When the population variance 2 is known, the 100 C % confidence interval for is given by: X- z * n , X + z * n where Pr(- z * Z z * ) = C . When the population variance 2 is unknown, the 100 C % confidence interval for is given by: X- t * s n , X + t * s n where Pr(- t * t n- 1 t * ) = C . For 95% CI, z * = 1 . 96 and t * depends on n- 1. Mugglin and Eberly PubH 6450 Fall 2011 Part 09 4 / 53 Review Revisiting Important Concepts Hypothesis Testing Back to arrow (3) Mugglin and Eberly PubH 6450 Fall 2011 Part 09 5 / 53 Review Revisiting Important Concepts Hypothesis Testing True State of Nature Parameters: , 2 , , , , p, Observations Sample Statistics: Mugglin and Eberly PubH 6450 Fall 2011 Part 09 6 / 53 Review Revisiting Important Concepts Hypothesis Testing Statistical inference Statistical inference is the process of drawing some conclusion about a population parameter using the information contained in a sample. We can use a CI to make a statement about the population parameter. Example: In Part 7, we calculated the 90% confidence interval for mean birthweight among female alcohol-exposed infants as (2.35,2.65). We can say that We are 90% confident that the mean birthweight for female alcohol-exposed infants lies between 2.35 kg and 2.65 kg. A CI is one tool for making statistical inference....
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This note was uploaded on 11/21/2011 for the course PUBH 6450 taught by Professor Andymugglin during the Fall '10 term at Minnesota.

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part9 - Public Health 6450 Fall 2011 Andrew Mugglin and...

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