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PDB_Stat_100_Lecture_19_Printable

# PDB_Stat_100_Lecture_19_Printable - STA 100 Lecture 19 Paul...

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STA 100 Lecture 19 Paul Baines Department of Statistics University of California, Davis February 18th, 2011

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Admin for the Day I Homework 5 Online – due Wednesday! I Midterms are not quite ﬁnished being graded. . . I Midterm solutions are posted I No class Monday – President’s Day! I Project details posted I Projects in groups of 4: Groups due Monday! I Project Proposals due Friday! References for Today: Rosner, Ch 7.1-7.7 (7th Ed.) References for Wednesday: Rosner, Ch 8 (7th Ed.)
Hypothesis Testing Last time we made the leap from conﬁdence intervals to hypothesis tests . A CI provides an interval that 100(1 - α )% of the time will contain the true value of the parameter (usually either μ or λ or p ). Hypothesis tests ask whether a speciﬁc value of the parameter (e.g., μ or λ or p ) is plausible, given the data. To decide this we decided that we would like a probability of 0.05 or less of seeing the result we saw (or more extreme). They are very much related. . .

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Example Example: (Rosner Ex7.2, Ch7) Recall the low birthweight babies example. Do babies born in a particular hospital weigh less than the national average? Does the area need a specialist care unit for premature babies? If babies do weigh less than there may be justiﬁcation for the specialist care unit. Let X i be the weight of baby i . Birth weights follow a normal distribution: X i N ( μ, σ 2 ). The national average birthweight is 120 oz.
Types of Error There are two possible TRUE situations: 1. The null hypothesis, H 0 , is true, or, 2. The null hypothesis, H 0 , is not true. There are two possible DECISIONS you can make: 1. Reject H 0 , or, 2. Do not reject H 0 . So there are four possible outcomes. . .

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Types of Errors H 0 True H 0 False Do not reject H 0 Correct! , Wrong. . . Type II Error Reject H 0 Wrong. . . Type I Error Correct! , Which are worse: type I or type II errors? It depends. Two situations: FDA licensing a new drug. Judge in a murder trial. I What are the null hypotheses in these examples? I In which example are type I errors are worse? I In which example where type II errors are worse? I What do the errors mean in the birthweight example?
Types of Error Some letters: I We denote the probability of a Type I error by α I We denote the probability of a Type II error by β The power of a test is deﬁned to be 1 - β . The

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PDB_Stat_100_Lecture_19_Printable - STA 100 Lecture 19 Paul...

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