8 Part of a research study of identical twins who had been separated at birth involved a random sample of 9 pairs, in which one twin had been raised by the natural parents and the other by adoptive parents. The IQ scores of these twins were measured, with the following results.
| Twin pair | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| IQ of twin raised by natural parents | 82 | 92 | 115 | 132 | 88 | 95 | 112 | 83 | 123 |
| IQ of twin raised by adoptive parents | 92 | 88 | 115 | 134 | 97 | 94 | 107 | 88 | 130 |
It may be assumed that the difference in IQ scores has a normal distribution. The mean IQ scores of separated twins raised by natural parents and by adoptive parents are denoted by \(\mu _ { N }\) and \(\mu _ { A }\) respectively. Obtain a \(90 \%\) confidence interval for \(\mu _ { N } - \mu _ { A }\).
One of the researchers claimed that there was no evidence of a difference between the two population means. State, giving a reason, whether the confidence interval supports this claim.