UT Knoxville STAT 201 - Chapter 24 (36 pages)

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Chapter 24 Chapter24 Presentation 1213 Comparing Means from Independent Samples Copyright 2009 Pearson Education Inc 1 Plot the Data A natural display for comparing two groups is boxplots of the data for the two groups placed sideby side For example Chapter24 Presentation 1213 Copyright 2009 Pearson Education Inc 2 Comparing Two Means Once we have examined the side by side boxplots of sample data we can turn to the comparison of the two population means The parameter of interest is the difference between the two population means 1 2 Chapter24 Presentation 1213 Copyright 2009 Pearson Education Inc 3 The Standard Error for Comparing Two Means For independent random quantities variances add standard deviations are not additive So the standard deviation of the difference between two sample means is SD y1 y2 12 n1 22 n2 We still don t know the true standard deviations of the two groups so we need to use the standard error s12 s22 SE y1 y2 n1 n2 Chapter24 Presentation 1213 Copyright 2009 Pearson Education Inc 4 Using t to Compare Two Means The sampling distribution of the difference in sample means of two independent groups is a Student s t The confidence interval we build is called a two sample t interval for the difference in means The corresponding hypothesis test is called a two sample t test Chapter24 Presentation 1213 Copyright 2009 Pearson Education Inc 5 Assumptions and Conditions Independence Assumption Each condition needs to be checked for both groups Randomization Condition Is the data from a random sample 10 Condition Were the samples for each group less than 10 of the respective populations Chapter24 Presentation 1213 Copyright 2009 Pearson Education Inc 6 Assumptions and Conditions cont Normal Population Assumption Nearly Normal Condition This must be checked for both groups A violation by either one violates the condition Independent Groups Assumption The two groups we are comparing must be independent of each other Chapter24 Presentation 1213 Copyright