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# Lecture15standard - Statistics 511 Statistical Methods Dr...

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Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 Lecture 14: Introduction to Hypothesis Testing Devore: Section 8.1 March, 2011 Page 1

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Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 What is statistical hypothesis? A statistical hypothesis is a claim about the value of a parameter(s) or about the form of a distribution as a whole. As an example, consider a normal distribution with the mean μ . Then, the statement μ = . 75 is a hypothesis. March, 2011 Page 2
Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 Null and Alternative Hypotheses Usually, two contradictory hypotheses are under consideration. For example, we may have μ = . 75 and μ 6 = . 75 . Alternatively, for a probability of success of some binomial distribution, we may have p . 10 and p . 10 . 1. The null hypothesis H 0 is the one that is initially assumed to be true. 2. The alternative hypothesis H a is the assertion contrary to H 0 . March, 2011 Page 3

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Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 We reject the null hypothesis in favor of the alternative hypothesis if the sample evidence suggests so. If the sample does not contradict H 0 , we continue to believe it is true. Thus, the two possible conclusions from a hypothesis-testing analysis are reject H 0 or fail to reject H 0 . March, 2011 Page 4
Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 An Example of the Test A test of hypothesis is a method for using sample data to decide whether the null hypothesis should be rejected. How exactly do we formulate a test? It depends on what our goals are. .. Consider a company that wants to introduce an expensive new

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Lecture15standard - Statistics 511 Statistical Methods Dr...

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