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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 head2right A (significance) test assumes that the data production used randomization head2right Other assumptions may include: Assumptions about the sample size or about the shape of the population distribution Step 2 : Hypotheses head2right 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 head2right The main goal in many research studies is to check whether the data support certain hypotheses head2right 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 xrhombus The hypotheses should be formulated before viewing or analyzing the data! Step 3: Test Statistic head2right A test statistic describes how far the point estimate falls from the parameter value given in the null hypothesis head2right 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 head2right 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 head2right 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 P-value
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