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# Outline Of Chapter 9 Text Elementary Statistics: A Brief Version(A. Bluman 3rd Ed., 2003)

1118 words - 4 pages

ObjectivesTest the difference between two large sample means using the z test.Test the difference between two variances or standard deviations.Objectives (cont'd.)Test the difference between two means for small independent samples.Test the difference between two means for small dependent samples.Test the difference between two proportions.The Difference Between Two MeansAssumptions for the test to determine the difference between two means:The samples must be independent of each other; that is, there can be no relationship between the subjects in each sample.The populations from which the samples were obtained must be normally distributed, and the standard deviations of the variable must be known, or the sample sizes must be greater than or equal to 30.FormulaFormula for the z test for comparing two means from independent populationsGeneral Formula FormatObserved differenceExpected differenceStandard error of differenceDifference Between Two MeansFor Large Samples:When n1" 30 and n2 " 30, and can be used in place of and .F DistributionIf two independent samples are selected from two normally distributed populations in which the variances are equal ( ) and if the variances are compared as ,the sampling distribution of the ratio of the variances is called the F distribution.Characteristics of the F DistributionThe values of F cannot be negative, because variances are always positive or zero.The distribution is positively skewed.The mean value of F is approximately equal to 1.The F distribution is a family of curves based on the degrees of freedom of the variance of the numerator and the degrees of freedom of the variance of the denominator.FormulaThe F test:where is the larger of the two variances.The F test has two terms for the degrees of freedoms: that of the numerator, n1-1, and that of the denominator, n2-1, where n1 is the sample size from which the larger variance was obtained.Notes for the Use of the F testThe larger variance should always be designated as and be placed in the numerator of the formula.For a two-tailed test, the a value must be divided by 2 and the critical value be placed on the right side of the F curve.Notes for the Use of the F test (cont'd.)If the standard deviations instead of the variances are given in the problem, they must be squared for the formula for the F test.When the degrees of freedom cannot be found in Table H, the closest value on the smaller side should be used.The Differences Between Two VariancesThe assumptions for testing the differences between two variances are:The populations from which the samples were obtained must be normally distributed. (Note: The test should not be used when the distributions depart from normality.)The samples must be independent of each other.t TestA t test is used to test the difference between means when the two samples are independent, when the sample sizes are small, and when the samples are taken from two normally or approximately normally distributed populations.There...

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