Chapter8

Chapter8 - Chapter 8 Inferences Based on a Single Sample:...

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Chapter 8 Inferences Based on a Single Sample: Tests of Hypothesis 8.1 The Elements of a Test of Hypothesis The objective of a statistical test is to test an hypothesis concerning the value of one or more population parameters. A statistical test involves the following four elements: 1. Null and alternative hypotheses : The purpose of hypothesis testing is to test the viability of the null hypothesis in the light of experimental data. The null hypothesis is the hypothesis about a population parameter. The alternative hypothesis is the hypothesis that the researchers wish to support. The null hypothesis is a contradiction of the alternative hypothesis. The null and alternative hypotheses are denoted by H 0 and H a respectively. Extra Example 1: Suppose we want to know whether the average income of the FIU students is $20,000. Then we have the following two-sided alternative. H 0 : μ =2 0 , 000 H a : μ ± 0 , 000 Extra Example 2: Suppose we want to know whether the average age of the FIU students exceeds 25 years (which is equivalent to say, not more than 25). Then we have the following one-sided (upper or right tailed test) alternative. H 0 : μ 25 H a : μ> 25 40
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Suppose we want to know whether the average age of the FIU students is less than 25 years (which is equivalent to say, at least 25). Then we have the following one-sided (lower or left tailed test) alternative. H 0 : μ 25 H a : μ< 25 2. Test statistic: A statistic computed from sample measurements that will be used to test the null hypothesis. OR, The sample quantity on which the decision to support H 0 or H a is based is called the test statistic. 3. Critical region or rejection region: The set of values of the test statistic that leads to rejection of the null hypothesis in favor of the alternative hypothesis is called the critical or rejection region. 4. Decision Rules: Reject H 0 at α % level of signi±cance, if the calculated value of the test statistic (observed value) falls in the rejection region. There are four possible outcomes of a test of hypothesis presented in Table 8.1. Table 8.1: Decision Table Truth about the population Decision based on sample Reject H 0 Do not Reject H 0 H 0 is true Type I Correct Decision H 0 is false Correct Decision Type II Type I and Type II Errors Two kinds of errors are committed when testing the hypotheses or making decision about the null hypothesis.
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Chapter8 - Chapter 8 Inferences Based on a Single Sample:...

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