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Hypothesis testing Chapter 9

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Introduction to Statistical Tests

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Stating Hypotheses Null hypothesis H 0 : This is the statement that is under investigation or being tested. Usually the null hypothesis represents a statement of “no effect”, “no difference”, or, put another way, “things haven’t changed”. Alternate hypothesis H 1 : This is the statement you will adopt in the situation in which the evidence (data) is so strong tat you reject H 0. A statistical test is designed to assess the strength of the evidence (data) against the null hypothesis. Null hypotheses are always of the form H 0 : some parameter = some value.

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Types of Tests A statistical test is: left-tailed if H 1 states hat the parameter is less than the cited value claimed in H 0. right-tailed if H 1 states hat the parameter is greater than the value claimed in H 0. two-tailed if H 1 states that the parameter is different from the value claimed in H 0.

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Hypothesis Tests of µ, Given that x is Normal and σ is Known

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The P-value of a Statistical Test P-value Assuming H 0 is true, the probability that the test statistic will take on values as extreme as or more extreme than the observed test statistic is called the P-value of the test. The smaller the P-value computed from sample data, the stronger the evidence against H 0. See pages 393, 394

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Types of Errors A type I error occurs if H 0 is true but we reject H 0 A type II error occurs if H 0 is false but we do not reject H 0 The level of significance α is the probability of rejecting H 0 when it is true. This is the probability of a type I error. The probability of making a type II error is denoted by the Greek letter β The quantity 1-β is called the power of a test and represents the probability of rejecting H 0 when it is false See table 9-3

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Concluding a Statistical Test If P-value ≤ α, we reject the null hypothesis and say the data are statistically significant at the level α If P-value > α, we do not reject the null hypothesis

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Testing the Mean µ

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Testing µ when σ is Known

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Testing µ when σ is Unknown

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Testing µ Using Critical Regions (Traditional Method)

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Testing a Proportion p

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How to test a Proportion p

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