Chapter-9_Note - Chapter 9: Statistical Inference:...

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1 Chapter 9: Statistical Inference: Significance Tests About Hypotheses Steps for Performing a Significance Test Significance Test: A significance test is a method of using data to summarize the evidence about a hypothesis. A significance test about a hypothesis has five steps. 1) Assumptions 2) Hypotheses 3) Test Statistic 4) P-value 5) Conclusion Step 1 : Assumptions h A (significance) test assumes that the data production used randomization h Other assumptions may include: Assumptions about the sample size or about the shape of the population distribution Step 2 : Hypotheses h A hypothesis is a statement about a population, usually of the form that a certain parameter takes a particular numerical value or falls in a certain range of values h The main goal in many research studies is to check whether the data support certain hypotheses h Each significance test has two hypotheses: The null hypothesis is a statement that the parameter takes a particular value. It has a single parameter value. The symbol H o denotes null hypothesis. This always has equality “=” sign. Ex: H 0 : p = 0.72 H 0 : μ = 42.3 The alternative hypothesis states that the parameter falls in some alternative range of values. The symbol H a denotes alternative hypothesis. The alternative hypothesis should express what the researcher hopes to show. This always has one of “>”, “<”, or “ ” signs. Ex: H a : p < 0.47 H a : μ 42 H a : μ > 3.45 x The hypotheses should be formulated before viewing or analyzing the data! Step 3: Test Statistic h A test statistic describes how far the point estimate falls from the parameter value given in the null hypothesis h We use the test statistic to assess the evidence against the null hypothesis by giving a probability, the P-Value. Step 4: P-value Alternative Hypothesis P-value h To interpret a test statistic value, we use a probability summary of the evidence against the null hypothesis, H o First, we presume that H o is true Next, we consider the sampling distribution from which the test statistic comes We summarize how far out in the tail of this sampling distribution the test statistic falls h We summarize how far out in the tail the test statistic falls by the tail probability of that value and values even more extreme This probability is called a
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This note was uploaded on 08/04/2011 for the course MATH 2300 taught by Professor Staff during the Spring '08 term at Texas Tech.

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Chapter-9_Note - Chapter 9: Statistical Inference:...

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