Expand Your Knowledge: Pooled Two-Sample Procedure

Chapter , Problem 22

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Expand Your Knowledge: Pooled Two-Sample Procedure Consider independent random samples from two populations that are normal or approximately normal, or the case in which both sample sizes are at least 30. Then, if s1 and s2 are unknown but we have reason to believe that s1 s2, we can pool the standard deviations. Using sample sizes n1 and n2, the sample test statistic has a Students t distribution, where with degrees of freedom and where the pooled standard deviation s is Note: With statistical software, select the pooled variance or equal variance options. (a) There are many situations in which we want to compare means from populations having standard deviations that are equal. This method applies even if the standard deviations are known to be only approximately equal (see Section 11.4 for methods to test that s1 s2). Consider regarding average incidence of fox rabies in two regions. For region I, n1 16, and s1 2.82 and for region II, n2 15, and s2 2.43. The two sample standard deviations are sufficiently close that we can assume s1 s2. Use the method of pooled standard deviation to redo 17, where we tested if there was a difference in population mean average incidence of rabies at the 5% level of significance. (b) Compare the t value calculated in part (a) using the pooled standard deviation with the t value calculated in using the unpooled standard deviation. Compare the degrees of freedom for the sample test statistic. Compare the conclusions.