Incorrect. A paired t-test (aka t-test for correlated means) is appropriate for data which is paired, matched, or before-after. In this case, we have 2 groups which we have no reason to believe constitute a "pair." Because our groups do not constitute a pair, we cannot use the paired t-test.
If, for example, we had collected data from Belize (24 families) and for each family, we had a family in Samoa that was exactly the same in terms of income, age of mother, age of child, size of community, etc. then, we could argue for a "paired" test. In this case, we have taken each family from 1 culture (Belize) and matched them with a family very similar to them in the other culture (Samoa). Since for each pair of families, we have made sure that they are the same, the only difference between the families can be attributed to culture.
In general, the paired designed is preferred but, it is often impractical.
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