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in making a decision about a parameter value rather then obtaining an estimate of its value8.2 Formulation of Hypotheses•A null hypothesisH0 is the hypothesis against which we hope to gather evidence. The hypothesis for which we wish to gather supporting evidence is called the alternative hypothesisesHa•One-tailed (directional) test and two-tailed test8.3 Conclusions and Consequences for a Hypothesis Test•The goal ofany hypothesis-testing is to make a decision based on sample information: whether to reject H0 in favor of Ha →we make one of two types of error.•A Type I error occurs if we reject H0 when it is true. The probability of committing a Type I error is denoted by α(also called significance level)•A Type II error occurs if we do not reject H0 when it is false. The probability of committing a Type II error is denoted by β.•Contents•[Back]
26Chapter 8 (continued 1)8.4 Test statistics and rejection regions•The test statisticis a sample ststistic, upon which the decision concerning the null and alternative hypotheses is based.•The rejection regionis the set of possible values of the test statistic for which the null hypotheses will be rejected.•Steps for testing hypothesis•Critical value =boundary value of the rejection region8.5 Summary8.6 Exercises•[Back]
27Chapter 9. Applications of Hypothesis Testing9.1 Diagnosing a hypothesis test9.2 Hypothesis test about a population mean9.3 Hypothesis test about a population proportion9.4 Hypothesis tests about the difference between two population means9.5 Hypothesis tests about the difference between two proportions9.6 Hypothesis test about a population variance9.7 Hypothesis test about the ratio of twopopulation variances9.8 Summary9.9 Exercises•[Back]•[Contents]
28Chapter 9 (continued 1)9.2 Hypothesis test about a population mean•Large- sample test(n>=30):–the sampling distribution of is approximately normal and s is a good approximation of σ.–Procedure for large- sample test •Small- sample test:–Assumption: the population ha aaprox. Normal distribution.–Procedure for small- sample test (using t-distribution)\9.3 Hypothesis test about a population proportionLarge- sample test9.4 Hypothesis tests about the difference between two population means•Large- sample test:–Assumptions: n1>=30, n2>=30; samples are selected randomly and independently from the populations•Small- sample test•[Back]
29Chapter 9 (continued 2)9.5 Hypothesis tests about the difference between two proportions:Assumptions, Procedure9.6 Hypothesis test about a population variance–Assumption: the population has an approx. nornal distr.–Procudure using chi-square distribution9.7 Hypothesis test about the ratio of twopopulation variances (optional)–Assumptions: Populations has approx. nornal distr., random samples are independent.