Part of a research study of identical twins who had been separated at birth involves a random sample of 9 pairs, in which one of the twin has been raised by the natural parent and the other by adoptive parents. The IQ scores of these twins were measured.
It maybe assumed that the difference in IQ has a normal distribution. The mean IQ scores of separated twins raised by natural parents and adoptive parent are denoted by $u_n$ and $u_a$
Obtain the confidence interval for $u_n-u_a$
The answer for this question treats the two samples as paired samples. How is this a paired sample instead of a separate two samples? My understanding for a paired sample is that if a SAME sample undergoes a transformation and provide different results then the different data are considered as a paired sample.
But in this case it's obvious that the twins are two different human beings and hence the result obtained using them constitutes to be two different samples.
Can somebody please explain the fallacy in my proposed statements?