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# An Analysis of the Difference Between Two Means

Objectives Test the difference between two large sample means using the z test Test the difference between two variances or standard deviations Objectives contd 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 Means Assumptions 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 Formula Formula for the z test for comparing two means from independent populations General Formula Format Observed difference Expected difference Standard error of difference Difference Between Two Means For Large Samples When n1 30 and n2 30 and can be used in place of and F Distribution If 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 Distribution The 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 Formula The F test where is the larger of the two

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