Two_Samples_Hypothesis_Testing - Two Samples Hypothesis...

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Two Samples Hypothesis Testing Author: John M. Cimbala, Penn State University Latest revision: 28 September 2007 Introduction In a previous learning module, we discussed how to perform hypothesis tests for a single variable x . Here, we extend the concept of hypothesis testing to the comparison of two variables x A and x B . B Two Samples Hypothesis Testing when n is the same for the two Samples In engineering analysis, we often want to test whether some modification to a system causes a statistically significant change to the system (either the system is improved or made worse). We conduct some experiments in which the sample mean A x of sample A (without the modification) is indeed different than the sample mean B x of sample B (with the modification). In other words, the modification appears to have led to a change, but is the change statistically significant? Here we discuss the simplest such statistical test – a test of whether one sample of data has a significantly different predicted population mean compared to a second sample of data, and with the number of data points n being the same in the two samples. Statisticians refer to this case (equal n in the two samples) as a paired samples hypothesis test . The procedure is very similar to the single-sample hypothesis tests we have already discussed, except that we replace variable x by the difference between the two variables , B A x x δ = . We restrict our discussion to the typical case where we want to know whether there is a statistically significant change in the predicted population means of the two samples. From the definition of variable , we see that an appropriate null hypothesis is = 0 , i.e., there is no change in the population mean between the two samples. Thus, we set: o Null hypothesis : Critical value is μ 0 = 0; the least likely scenario is = 0 (there is no statistically significant change in the population means). [This is the least likely scenario since AB x x .] o
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This note was uploaded on 07/23/2008 for the course ME 345 taught by Professor Staff during the Spring '08 term at Pennsylvania State University, University Park.

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Two_Samples_Hypothesis_Testing - Two Samples Hypothesis...

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