Lecture18standard - Statistics 511 Statistical Methods Dr Levine Purdue University Spring 2011 Lecture 17 P-values and some Additional Issues

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Unformatted text preview: Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 Lecture 17: P-values and some Additional Issues concerning Testing Devore: Section 8.4-8.5 April, 2011 Page 1 Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 The Need for P-values • There are two main problems with the rejection region based approach to testing: 1. It says nothing about where exactly the value of test statistic fell in the rejection region. 2. It imposes the specified significance level on other decision makers April, 2011 Page 2 Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 Example I • Discarded batteries are a significant source of urban storm water contamination (especially in terms of zinc). A sample of 51 Panasonic AAA batteries gave a sample mean zinc mass of 2 . 06 g and a sample standard deviation of . 141 g. Does this data provide compelling evidence for concluding that the population mean zinc mass exceeds 2 . g? • The hypotheses involved are H : μ = 2 . vs. H a : μ > 2 . • The test statistic is z = ¯ x- 2 . s √ n = 3 . 04 April, 2011 Page 3 Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 Example II • The values of ¯ x that are at least as contradictory to the null hypothesis as 2 . 06 are all those that exceed 2 . 06 . They correspond to the values of z that exceed 3 . 04 • The probability that the sample-based statistic z exceeds the current value under the null hypothesis is P ( Z > 3 . 04 when μ = 2 . 0) = 1- Φ(3 . 04) = 0 . 012 April, 2011 Page 4 Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 P-value definition • The P-value is the probability, calculated assuming that the null hypothesis is true, of obtaining a value of the test statistic at least as contradictory to H as the value calculated from the available sample. • Important points: 1. The P-value is a probability 2. This probability is calculated assuming that the null hypothesis is true 3. The P-value is NOT the probability that H is true, nor is it an error probability April, 2011 Page 5 Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 Decision rule based on the P-value • Clearly, if the significance level chosen is α , then 1. Reject H if P-value ≤ α 2. Do not reject H if P-value > α April, 2011 Page 6 Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 Example • The nicotine content problem involves testing...
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This note was uploaded on 02/20/2012 for the course STAT 511 taught by Professor Bud during the Fall '08 term at Purdue University-West Lafayette.

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Lecture18standard - Statistics 511 Statistical Methods Dr Levine Purdue University Spring 2011 Lecture 17 P-values and some Additional Issues

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