Incorrect. This hypothesis is correct in form and could be a valid hypothesis for the data if our informal hypothesis was simply that both groups were not equal. This what we have stated in the alternative hypothesis here. However, we want to determine whether children in Belize are closer to their mothers than children in Samoa; this should be the alternative hypothesis.

If we were only interested stating that the two groups were different (i.e. a two-tailed test), the hypothesis you have chosen would be the correct hypothesis.