# 3 - Hypothesis Testing basic ingredients of a hypothesis...

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Hypothesis Testing basic ingredients of a hypothesis test are 1. the null hypothesis , denoted H o 2. the alternative hypothesis , denoted H a 3. the test statistic 4. the the data 5. the conclusion the hypotheses are usually statements about the values of one or more unknown parameters, denoted θ here the null hypothesis is usually a more restrictive statement than the alter- native hypothesis, e.g. H o : θ = θ o , H a : θ 6 = θ o the burden of proof is on the alternative hypothesis we will continue to believe in the null hypothesis unless there is very strong evidence in the data to refute it the test statistic measures agreement of the data with the null hypothesis a reasonable combination of the data and the hypothesized value of the parameter gets bigger when the data agrees less with the null hypothesis when ˆ θ is an estimator for θ with standard error s ˆ θ , a common test statistic has the form z = ˆ θ - θ o s ˆ θ when the data agrees perfectly with the null hypothesis, z = 0 when the estimated and hypothesized values for θ become farther apart, z increases in magnitude there are two closely related approaches to testing

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3 - Hypothesis Testing basic ingredients of a hypothesis...

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