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# 6.2 - (6.2 Testsofsignificance Hypothesistesting Use sample...

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Introduction to inference (6.2)  Tests of significance

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Hypothesis testing Use sample data to decide on the validity of a hypothesis.
Lady tasting tea   Given a cup of tea with milk, a lady claims she can discriminate as to whether milk or tea was first added to the cup. To test her claim, eight cups of tea are prepared, four of which have the milk added first and four of which have the tea added first. Put the eight cups of tea in random order. The lady tastes the teas and selects 4 cups, the ones she claims to have had the tea poured first.

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Suppose the lady correctly identifies all 4 cups. Is this purely due to chance or that she indeed has discriminatory ability? This can be formulated as a hypothesis testing problem. Hypothesis: The lady has no discriminatory ability.
You are in charge of quality control in a food company. You sample randomly four packs of cherry tomatoes, each labeled 1/2 lb. (227 g). The average weight from your four boxes is 222 g. Obviously, we cannot expect boxes filled with whole tomatoes to all weigh exactly half a pound. Thus, Is the somewhat smaller weight simply due to chance variation? Is it enough evidence that the calibrating machine that sorts cherry tomatoes into packs needs revision? The same question rephrased statistically: Is the population mean µ for the distribution of weights of cherry tomato packages equal to 227 g (i.e., half a pound)?

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Two hypotheses: H 0 : µ = 227 g Null hypothesis H a : µ ≠ 227 g Alternative hypothesis, Where µ is the average weight of the population of packs of cherry tomatoes. With equal to 222, can we say that µ is different from 227?
Null hypothesis The statement being tested is called a null hypothesis. The test is designed to assess the strength of the evidence against the null hypothesis. Usually the null hypothesis is a statement of “no effect” or “no difference”.

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One-sided and two-sided tests A two-tail or two-sided test of the population mean has these null and alternative hypotheses: H 0 : µ = [a specific number] H a : µ [a specific number] A one- tail or one-sided test of a population mean has these null and alternative hypotheses: H 0 : µ = [a specific number] H a : µ < [a specific number] OR H 0 : µ = [a specific number] H a : µ > [a specific number]
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