Complex Samples Dependent Z-Test - Comparing a Sub-Group Mean to Total

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Where is the mean in the total sample and is the mean in the sub-group, and are their respective effective sample sizes, and is the proportion of the total population in sub-group :

,

where:

,
,
,
,
,
is the Standard Error of ,
is 1 if Bessel's correction is selected for Proportions in Statistical Assumptions and 0 otherwise,
and are the estimated standard deviations for the total sample and sub-groups respectively,
and are the estimated standard error of the means for the total sample and sub-groups respectively,
is Extra Deff, and
is the proportion of the Population represents by the sub-group.