Statistical Inference ch3

# Statistical Inference ch3 - Topic Three Inferences about a...

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MSOR221 1 / 5 Topic Three Inferences about a Population: Hypothesis Testing Hypothesis testing is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement and should not be rejected, or is unreasonable and should be rejected. The Classical Approach to Hypothesis Testing 1. Formulate the null and alternative hypothesis. 2. Decide on the level of significance. 3. Determine the appropriate test statistic (or probability distribution). 4. Find the critical value(s) and then establish the decision rule. 5. Compute the value of the test statistic from sample information and make the statistical decision. 6. State the conclusion in words (or in the language of the problem). 1. Formulate the Null and Alternative Hypotheses - The null hypothesis H 0 is the hypothesis that is always tested. - The alternative hypothesis H 1 is set up as the opposite of the null hypothesis and represents the conclusion supported if the null hypothesis is rejected. Inequality Sign Null Hypothesis H 0 = Alternative Hypothesis H 1 < > The statement of the null hypothesis always contains an equal sign regarding the specified value of the parameter. The statement of the alternative hypothesis never contains an equal sign regarding the specified value of the parameter. The null hypothesis always refers to a specified value of the population parameter, not a sample statistic.

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MSOR221 2 / 5 2. Decide on the Level of Significance - The significance level, α , of a hypothesis test is defined as the probability of making a Type I error, that is, the probability of rejecting a true null hypothesis. In hypothesis testing four outcomes are possible, two of which lead to incorrect decisions. Actual Situation
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## Statistical Inference ch3 - Topic Three Inferences about a...

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