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Outline Of Chapter 8 Text Elementary Statistics: A Brief Version(A. Bluman 3rd Ed., 2003)

1375 words - 6 pages

ObjectivesUnderstand the definitions used in hypothesis testing.State the null and alternative hypotheses.Find critical values for the z test.State the five steps used in hypothesis testing.Test means for large samples using the z test.Test means for small samples using the t test.Objectives (cont'd.)Test proportions using the z test.Test variances or standard deviations using the chi square test.Test hypotheses using confidence intervals.Explain the relationship between type I and type II errors and the power of a test.IntroductionStatistical hypothesis testing is a decision-making process for evaluating claims about a population.In hypothesis testing, the researcher must define the population under study, state the particular hypotheses that will be investigated, give the significance level, select a sample from the population, collect the data, perform the calculations required for the statistical test, and reach a conclusion.Hypothesis TestingHypotheses concerning parameters such as means and proportions can be investigated.The z test and the t test are used for hypothesis testing concerning means.Methods to Test HypothesesThe three methods used to test hypotheses are:1. The traditional method.2. The P-value method.3. The confidence interval method.Statement of a HypothesisA statistical hypothesis is a conjecture about a population parameter which may or may not be true.There are two types of statistical hypotheses for each situation: the null hypothesis and the alternative hypothesis.HypothesesThe null hypothesis, symbolized by H0, is a statistical hypothesis that states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters.The alternative hypothesis, symbolized by H1, is a statistical hypothesis that states the existence of a difference between a parameter and a specific value, or states that there is a difference between two parameters.Hypothesis-Testing Common PhrasesDesign of the StudyAfter stating the hypotheses, the researcher's next step is to design the study. The researcher selects the correct statistical test, chooses an appropriate level of significance, and formulates a plan for conducting the study.Statistical TestA statistical test uses the data obtained from a sample to make a decision about whether or not the null hypothesis should be rejected.The numerical value obtained from a statistical test is called the test value.Possible Outcomes of a Hypothesis TestSummary of Possible OutcomesA type I error occurs if one rejects the null hypothesis when it is true.A type II error occurs if one does not reject the null hypothesis when it is false.Error ProbabilitiesThe level of significance is the maximum probability of committing a type I error. This probability is symbolized by a; that is , .The probability of a type II error is symbolized by b. That is, .a and b ProbabilitiesIn most hypothesis testing situations, b cannot easily be computed; however, a and b are...

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