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Suppose you conduct a study and intend to use a hypothesis test to compare the means of two independent populations. Your null hypothesis is that the two means are equal. That is, H0: in = p2, or equivalently, H0: p1 p2 = 0. Following is a table of the information you gather. Assume the populations from which your samples are drawn are both normally distributed. Sample Size Sample Mean Sample Variance Sample 1 m = 21 i1 = 27.6 s'f' = 20.25 Sample 2 112 = 11 i2 = 21.5 s3 = 30.25 If the population variances are known (6% = 20.89 and 6% = 31.48), then the standard error of i1 i2 is V . When conducting a hypothesis test to compare the means, the test statistic is V . The appropriate degrees of freedom to use for the Student t distribution is v If the population variances are unknown but assumed to be equal (a? = 6%), then the estimated standard error of i1 i2 is v . When conducting a hypothesis test to compare the means, the test statistic is v . The appropriate degrees of freedom to use for the Student t distribution is v . If the population variances are unknown, but assumed to be unequal (012 at 012), then the estimated standard error of i1 i2 is V . When conducting a hypothesis test to compare the means, the test statistic is v . The appropriate degrees of freedom to use for the Student t distribution is V