This hypothesis is incorrect.
1) Our null hypothesis is never "does not equal." There is always some form of equal sign (either equal, more than or equal to, or less than or equal to) in our null hypothesis. This is because our t-test is testing how different (or unequal) or means are with the initial assumption that the two groups are equal.
2) Our alternative hypothesis (what we want to say, i.e. the informal hypothesis we stated before) does not reflect our hypothesis. The alternative hypothesis should be equivalent to the hypothesis we stated previous (that children in Belize were closer to their mothers than children in Samoa). Our hypothesis here states that the 2 groups are equal; this is not what we want to be able to conclude about the data.