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Unformatted text preview: AMS312 Spring_2010 April 12 th 1. Review: Inference on one population mean, normal population, population variance unknown (Quiz 5 Solutions): Approach 1 – Pivotal Quantity Method Hypothesis: : : a H H μ μ μ μ = : : a H H μ μ μ μ = < : : a H H μ μ μ μ = ≠ Now the pivotal quantity is: 1 / n X T t S n μ = : Exactly Test statistic: 1 ~ / H n X T t S n μ = For the first case, we reject H if 1, n T t α ≥ at the significance level α . For the second case, we reject H if 1, n T t α ≤  at the significance level α . For the last case, we reject H if 1, 2 n T t α ≥ at the significance level α . 1 AMS312 Spring_2010 William S. Gosset (1876 1937), inventor of the Student’s tdistribution. Example 1: Pica is a children’s disorder characterized by a craving for nonfood substances such as clay, plaster, and paint. Anyone affected runs the risk of ingesting high levels of lead, which can result in kidney damage and neurological dysfunction. Checking a child’s blood lead level is a standard procedure for diagnosing the condition. Among children between the ages of six months and five years, blood lead levels of 16.0mg/l are considered “normal”. Recently, a random sample of twelve children enrolled in Molly’s Mighty Bear Nursery had their blood lead levels checked. The resulting sample mean and sample standard derivation were 18.65 and 5.049, respectively. Can it be concluded that children at this particular facility tend to have higher lead levels? At the 0.05 α = level, is the increase from 16.0 to 18.65 statistically significant?...
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 Spring '08
 Zhu,W
 Statistics, Normal Distribution, Standard Deviation, Statistical hypothesis testing, significance level

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