# In making a decision about a parameter value rather

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in making a decision about a parameter value rather then obtaining an estimate of its value 8.2 Formulation of Hypotheses A null hypothesis H 0 is the hypothesis against which we hope to gather evidence. The hypothesis for which we wish to gather supporting evidence is called the alternative hypothesises H a One-tailed (directional) test and two-tailed test 8.3 Conclusions and Consequences for a Hypothesis Test The goal of any hypothesis-testing is to make a decision based on sample information: whether to reject H 0 in favor of H a we make one of two types of error. A Type I error occurs if we reject H 0 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 H 0 when it is false. The probability of committing a Type II error is denoted by β . •Contents •[Back]
26 Chapter 8 (continued 1) 8.4 Test statistics and rejection regions The test statistic is a sample ststistic, upon which the decision concerning the null and alternative hypotheses is based . The rejection region is 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 region 8.5 Summary 8.6 Exercises •[Back ]
27 Chapter 9. Applications of Hypothesis Testing 9.1 Diagnosing a hypothesis test 9.2 Hypothesis test about a population mean 9.3 Hypothesis test about a population proportion 9.4 Hypothesis tests about the difference between two population means 9.5 Hypothesis tests about the difference between two proportions 9.6 Hypothesis test about a population variance 9.7 Hypothesis test about the ratio of two population variances 9.8 Summary 9.9 Exercises •[Back] •[Contents]
28 Chapter 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 proportion Large- sample test 9.4 Hypothesis tests about the difference between two population means Large- sample test : Assumptions: n 1 >=30, n 2 >=30; samples are selected randomly and independently from the populations Small- sample test •[Back ]
29 Chapter 9 (continued 2) 9.5 Hypothesis tests about the difference between two proportions: Assumptions, Procedure 9.6 Hypothesis test about a population variance Assumption: the population has an approx. nornal distr. Procudure using chi-square distribution 9.7 Hypothesis test about the ratio of two population variances (optional) Assumptions: Populations has approx. nornal distr., random samples are independent.
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