Click to edit Master subtitle styleChapter 9 Introduction to thet statisticSpring 2010

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Thet Statistic•The t statistic allows researchers to use sample data to test hypotheses about an unknown population mean. •Advantage of the t statistic: does not require any knowledge of the population standard deviation. •Is used to test hypotheses about a completely unknownpopulation; that is, both μand σare unknown, and the only available information about the population comes from the sample.

The t Statistic (cont.)•All that is required for a hypothesis test witht is a sample and a reasonable hypothesis about the population mean. •There are two general situations where this type of hypothesis test is used:

The tStatistic (cont.)1.When a researcher wants to determine whether or not a treatment causes a change in a population mean. 2.To compare an actual sample mean with a hypothesized population mean. NOTE: when you know σ, compute a z-score, when you don’t, compute a t-statistic

μ

The Estimated Standard Error and the t Statistic (cont.)The hypothesis test attempts to decide between the following two alternatives:1.Is it reasonable that the discrepancy between M and μis simply due to sampling error and not the result of a treatment effect? 2.Is the discrepancy between M and μmore than would be expected by sampling error alone? That is, is the sample mean significantly different from the population mean?