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L22 - Testing a Single Parameter Signicance tests are...

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Testing a Single Parameter Significance tests are different type of statisti- cal inference. Want to choose between com- peting hypotheses about a parameter. θ Definition: An hypothesis is an assertion about a population or about a parameter. We distinguish two kinds of hypotheses: H 0 : null hypothesis (status quo, previously accepted) H 1 : alternative hypothesis (what you hope to establish) A significance test is a procedure for judging which hypothesis is true. 1
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Criminal trial analogy (in Canada, U.S.A.): H 0 : not guilty H 1 : guilty Not treated symmetrically. Assume H 0 true unless compelling evidence against H 0 in favour of H 1 . Likewise, in statistics H 0 is assumed true and is only rejected in favor of H 1 if the evidence (data) is compelling ( significant ) beyond rea- sonable doubt (could not happen by chance). 2
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Example. p 248 . Standard production setup, average μ = 30 minutes to com- plete task. Variation: work conditions, parts, ability leads to random error . X i is time taken by randomly selected worker i . X i = 30 + ε i . Assume ε i
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