## Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 9 summary

STEPS FOR PERFORMING A SIGNIFICANCE TESTA hypothesis is a statement about the population. A significance test is a method for using data to summarize the evidence about a hypothesis. The null hypothesis (H0) is a statement that the parameter takes a particular value (e.g: probability of getting a baby girl: p = 0.482). The alternative hypothesis (Ha) states that the parameter falls in some alternative range of values. A significance test has five steps:AssumptionsEach significance test has certain assumptions or has certain condition under which it applies (e.g: an assumption is the assumption that random sampling has been used).HypothesesEach significance test has two hypotheses about a population parameter. The null hypothesis and the alternative hypothesis.Test statisticThe parameter to which the hypotheses refer has a point estimate. A test statistic describes how far that point estimate falls from the parameter value given in the null hypothesis. This is usually measured in number of standard errors between the point estimate and the parameter.P-valueA probability summary of the evidence against the null hypothesis is used to interpret a test statistic. The P-value is the probability that the test statistic equals the observed value or a value even more extreme. It is calculated by presuming that the null hypothesis is true.ConclusionThe conclusion of the significance test reports the P-value and interprets what is says about the question that motivated the test.SIGNIFICANCE TESTS ABOUT PROPORTIONSThe steps for the significance test are the same for proportions. The biggest assumption made here is that the sample size is large enough that the sampling distribution is approximately normal. The hypotheses are the following for significance tests about proportions: and or This is called a one-sided alternative hypothesis, because it has values falling only on one side of the null hypothesis value. A two-sided alternative...

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