5. Comparing the means of two independent populations when the population variances are known, unknown and equal, and unknown and unequal
Suppose vou conduct study and intend to use hypothesis test to compare the means of two independent populations; Your null hypothesis is that the two means are equal: That is, Ho: Ht Hz, or equivalently, Ho: H1 Following is table of the information vou gather: Assume the populations from which your samples are drawn are both normally distributed_
Sample Size Sample Mean
Sample Variance
Sample
ni = 41
X1 = 14.3
67.24
Sample
X2 = 13.6
46.24
If the population variances are known (G3 = 67.88 ad G; = 47.47), then the standard error of X1 Xz is When conducting hypothesis test to compare the means_ the test statistic is The ppropriate degrees of freedom to use for the Student distribution is
If the population variances are unknown but assumed to be equal (63 conducting hypothesis test to compare the means_ the test statistic is distribution is
then the estimated standard error of X[ Xz Is
When
The appropriate degrees of freedom to use for the Student
If the population variances are unknown; but assumed to be unequal (of conducting hypothesis test to compare the means_ the test statistic is distribution is
then the estimated standard error of X]- Xz is The appropriate degrees of freedom to use for the Student
When