Analyzing the hypothesis, A recent report hypothesized that | Homework Helpers

A recent report hypothesized that the IQ of children that are first-born differs from those that are born later.  They found that first-born children have higher IQ’s than later born children, but you don’t believe this is correct.  To test this hypothesis, your classmates in statistics provide you their IQ scores and those of one of their siblings, and they tell you whether they are the first-born or their sibling was the first-born.  You want to compare these data to the recently published report to see if you get the same result. What test would you use to examine this hypothesis?  State the null and alternative hypotheses.  Do this problem two different ways:  Parametrically (all assumptions met), and nonparametrically.

The measures of IQ are, ? = 100 and ? = 15.  What is the likelihood of drawing a sample of people like that in the first column above, and the likelihood of drawing a sample of people like those in the second column?  For both columns separately, are the IQ scores greater than average as compared to the population at large?